
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
How many planes?

The Absent-Minded Scientist’s work involves long business trips, so he often flies with the same airline. This airline has many identical planes, all of which have names. Because the Scientist does not travel every day or even every week, it can be assumed that each time, he ends up on a random plane. Out of curiosity and habit, the Absent-Minded Scientist records the name of the plane he flies each time. On his fifteenth flight, the Scientist found himself on a plane proudly named "Siméon Denis Poisson." After takeoff, the Scientist took out his notebook to record the plane's name and discovered that he had already flown on "Poisson" once before, and there had been no repetitions prior to this. Estimate the number of planes in the airline's fleet.

Present the answer in LaTex format: \boxed{Your answer}
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