
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
Given that \( f(x) \) is an even function defined on all real numbers with the expression \( -x^{2} + 1 \) for \( x \in (-2, 2] \) and its graph is symmetric about \( x = 2 \), determine the expression for \( f(x) \) when \( x \in (-6, -2) \).

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