
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 the function $f(x+1)$ is an odd function defined on $\mathbb{R}$, if for any given distinct real numbers $x_1$ and $x_2$, the inequality $(x_1 - x_2)[f(x_1) - f(x_2)] < 0$ always holds, find the solution set for the inequality $f(1-x) < 0$.

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