
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 line $x=1$, and its derivative is $f'(x)$. When $x < 1$, $2f(x)+(x-1)f'(x) < 0$. Find the solution set of the inequality $(x+1)^{2}f(x+2) > f(2)$.

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