
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

Elmo calls a monic polynomial with real coefficients tasty if all of its coefficients are in $[-1,1]$. A monic polynomial \(P\) with real coefficients and complex roots \(\chi_{1}, \ldots, \chi_{m}\) (counted with multiplicity) is given to Elmo, and he discovers that there does not exist a monic polynomial \(Q\) with real coefficients such that \(P \cdot Q\) is tasty. Find all possible values of \(\max \left(\left|\chi_{1}\right|, \ldots,\left|\chi_{m}\right|\right)\).

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