
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
Let the function \( f(x) = ax^2 + bx + c \) where \( a \neq 0 \) satisfy \( |f(0)| \leq 2 \), \( |f(2)| \leq 2 \), and \( |f(-2)| \leq 2 \). Determine the maximum value of \( y = |f(x)| \) for \( x \in [-2, 2] \).

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