
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 trinomial \( f(x)=a x^{2}+b x+c \), where \( a>0 \), the condition \( |f(1)|=|f(2)|=|f(3)|=4 \) holds. What can its coefficients be?

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