
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 $f(x)$, where $x \in \mathbb{R}$, satisfying the following conditions: (1) $f(1 + x) = f(1 - x)$, (2) $f(x)$ is increasing on the interval $[1, +\infty)$, and (3) $x_1 < 0$, $x_2 > 0$ and $x_1 + x_2 < -2$, compare the magnitude of $f(-x_1)$ and $f(-x_2)$.

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