
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
Given that a human has fewer than 300,000 hairs and that there are 3,000,000 Parisians, at least two Parisians have the same number of hairs. One can even specify that there are at least 10 Parisians with the same number of hairs. If there were 3,000,001 Parisians, each with at most 300,000 hairs, one could assert that at least 11 of them have the same number of hairs.

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