
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 airplanes? (From the 11th grade, 8 points)

The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Since the Scientist does not fly every day and not even every week, it can be assumed that each time he is assigned a random airplane. Out of curiosity and out of habit, every time, the Absent-minded Scientist records the name of the airplane he flies on. On his fifteenth flight, the Scientist found himself on board an airplane proudly named "Siméon Denis Poisson." After takeoff, the Scientist pulled out his booklet to record the airplane's name and discovered that he had already flown on "Poisson" once before, and previously there had been no repetitions. Estimate the number of airplanes in the airline.

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