
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 a function \( f(x) \) defined on the set of real numbers \(\mathbf{R}\) that satisfies: 
1. \( f(-x) = f(x) \)
2. \( f(4-x) = f(x) \)

For \( x \in [0, 2] \), \( f(x) = -x^2 + 1 \). Determine \( f(x) \) for \( x \in [-6, -4] \).

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