
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
Define a function $f(x)$ on $\mathbb{R}$ that satisfies $(x-1)f'(x) \leq 0$, and $y=f(x+1)$ is an even function. When $|x_1 - 1| < |x_2 - 1|$, determine the relationship between $f(2-x_1)$ and $f(2-x_2)$.

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