
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 domain of the function $f(x)$ is $\mathbb{R}$, its graph is symmetric about the point $(1,0)$, and its derivative is $f′(x)$. When $x < 1$, $(x-1)[f(x)+(x-1)f′(x)] > 0$. Determine the solution set for the inequality $xf(x+1) > f(2)$.

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