NEW YORK (AP) -- They have seen him smiling on a hostel security camera, but don't know his name. They found the backpack he discarded while fleeing, but don't know where he's gone.

As the search for UnitedHealthcare CEO Brian Thompson's killer goes on, investigators are reckoning with a tantalizing dichotomy: They have troves of evidence, but the shooter remains an enigma.

Police don't know who he is, where he is, or why he did it -- though they are confident that it was a targeted attack instead of a random act.

"The net is tightening," New York City Mayor Eric Adams said Saturday.

Hours after he spoke, police divers were seen searching a pond in Central Park, where the killer fled after the shooting. Officers have been scouring the park for days for any possible clues and found his bag there Friday.

Retracing the gunman's steps using surveillance video, police say, it appears he left the city by bus soon after the shooting Wednesday morning outside the New York Hilton Midtown. He was seen on video at an uptown bus station about 45 minutes later, NYPD Chief of Detectives Joseph Kenny said.

With the high-profile search expanding across state lines, the FBI announced late Friday that it was offering a $50,000 reward for information leading to an arrest and conviction, adding to a reward of up to $10,000 that the NYPD has offered. Police say they believe the suspect acted alone.

Police provided no updates on the hunt Saturday, but investigators are urging patience -- even with a killer on the loose.

Hundreds of detectives are combing through video recordings and social media, vetting tips from the public and interviewing people who might have information, including Thompson's family and coworkers and the shooter's randomly assigned roommates at the Manhattan hostel where he stayed.

"This isn't 'Blue Bloods.' We're not going to solve this in 60 minutes," Kenny told reporters Friday. "We're painstakingly going through every bit of evidence that we can come across."

The shooter paid cash at the hostel, presented what police believe was a fake ID and is believed to have paid cash for taxi rides and other transactions. He didn't speak to others at the hostel and almost always kept his face covered with a mask, only lowering it while eating.

But investigators caught a break when they came across security camera images of an unguarded moment in which he briefly showed his face soon after arriving in New York on Nov. 24.

Police distributed the images to news outlets and on social media but so far haven't been able to ID him using facial recognition -- possibly because of the angle of the images or limitations on how the NYPD is allowed to use that technology, Kenny said.

On Friday evening, investigators found a backpack in Central Park that had been worn by the gunman, police said. They didn't immediately reveal what, if anything, it contained but said it would be tested and analyzed.

Another potential clue, a fingerprint on an item he purchased at a Starbucks minutes before the shooting, has so far proven useless for identifying him, Kenny said.

Aided by surveillance cameras on nearly every building and block, police have been able to retrace the shooter's movements.

They know he ambushed Thompson at 6:44 a.m. as the executive arrived at the Hilton for his company's annual investor conference, using a 9 mm pistol that resembled the guns farmers use to put down animals without causing a loud noise. They know ammunition found near Thompson's body bore the words "delay," "deny" and "depose," mimicking a phrase used by insurance industry critics.

Kenny said the fact that the shooter knew UnitedHealthcare group was holding a conference at the hotel and what route Thompson might take to get there suggested that he could possibly be a disgruntled employee or client.

Investigators know from surveillance video that the shooter fled into Central Park on a bicycle and ditched it around 7 a.m. near 85th Street.

He then walked a couple blocks and got into a taxi, arriving at 7:30 a.m. at the George Washington Bridge Bus Station, which is near the northern tip of Manhattan and offers commuter service to New Jersey and Greyhound routes to Philadelphia, Boston and Washington.

Investigators don't know what happened next. They are searching through more surveillance video but have yet to locate video of the shooter getting on a bus or exiting the station.

"We have reason to believe that the person in question has left New York City," Police Commissioner Jessica Tisch told CNN on Friday.

Police have determined from video that the gunman was in the city for 10 days before the shooting. He arrived at Manhattan's main bus terminal on a Greyhound bus that originated in Atlanta, though it's not clear whether he embarked there or at one of about a half-dozen stops along the route.

Immediately after that, he took a cab to the vicinity of the Hilton and was there for about a half hour, Kenny said.

At around 11 p.m. on the night he arrived, he went by taxi to the HI New York City Hostel. It was there, while speaking with an employee in the lobby, that he briefly pulled down the mask and smiled, giving investigators the brief glimpse they are now relying on to identify and capture a killer.

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Associated Press writers Michael Balsamo in Washington, Jake Offenhartz, Cedar Attanasio and Karen Matthews in New York, John Seewer in Toledo, Ohio, and Jeff Martin in Atlanta contributed.