
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? (11th grade, 8 points) The Absent-Minded Scientist's job involves long business trips, so he often flies with planes from the same airline. This airline has many identical planes, and all of them have names. Since the Scientist does not fly every day and not even every week, it can be assumed that each time he gets a "random" plane. Out of curiosity and habit, the Absent-Minded Scientist notes each time which plane he flies on. On his fifteenth flight, the Scientist found himself aboard a plane proudly named "Simeon Denis Poisson". After takeoff, the Scientist took out his notebook to record the plane's name and discovered that he had already flown on the "Poisson" once before, and there had been no repetitions prior. Estimate the number of planes in the airline.

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