
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
A quadratic polynomial with real coefficients and leading coefficient 1 is termed **bold** if the equation \( p(p(x)) = 0 \) is satisfied by exactly four real numbers. Identify the bold quadratic polynomial \( p(x) \) for which the product of the roots is minimized, and then determine the value of \( p(0) \).

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