
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
Define munificence for a polynomial $p(x)$ as the maximum absolute value of $p(x)$ on the interval $-1 \le x \le 1.$ Find the smallest possible munificence for a monic cubic polynomial of the form $p(x) = x^3 + px + q.$

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