
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
For the quadratic polynomial \( f(x) = ax^2 + bx + c \), where \( a > 0 \), the condition \( |f(1)| = |f(2)| = |f(3)| = 2 \) holds. What can its coefficients be?

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