
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 an odd function $f(x)$ with the domain of $\mathbb{R}$, whose graph is a continuous curve, when $x \in (1, +\infty)$, $f'(x) < 0$; when $x \in (0,1)$, $f'(x) > 0$, and $f(2)=0$, find the solution set of the inequality $(x+1)f(x) > 0$.

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