
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
Find all polynomials \( Q(x) = ax^2 + bx + c \) with integer coefficients such that three different primes \( p_1, p_2, p_3 \) exist with

\[ \left| Q(p_1) \right| = \left| Q(p_2) \right| = \left| Q(p_3) \right| = 11. \]

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