
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 domain $\mathbb{R}$ that satisfies $f(4-x) = -f(x)$, and $f(x)$ is monotonically decreasing when $x < 2$. If $x_1 + x_2 > 4$ and $(x_1 - 2)(x_2 - 2) < 0$, calculate the value of $f(x_1) + f(x_2)$.

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