
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
Let  $n$  be a positive integer and let  $P$  be the set of monic polynomials of degree  $n$  with complex coefficients. Find the value of 
\[ \min_{p \in P} \left \{ \max_{|z| = 1} |p(z)| \right \} \]

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