
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 \( f(x) \) with a domain of \( \mathbf{R} \) that satisfies \( f(-x) = -f(x+4) \), and is monotonically increasing when \( x > 2 \), if \( x_1 + x_2 < 4 \) and \( (x_1 - 2)(x_2 - 2) < 0 \), determine the sign of \( f(x_1) + f(x_2) \) and provide a proof.

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