
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 $x_0$ is a root of the function $f(x) = 3^x + \frac{2}{1-x}$, if $x_1 \in (1, x_0)$ and $x_2 \in (x_0, +\infty)$, determine the signs of $f(x_1)$ and $f(x_2)$.

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