
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
The function $f(x)$ is a differentiable function defined on the interval $(0,+\infty)$, with its derivative being $f'(x)$. It satisfies $f'(x) + \frac{2}{x}f(x) > 0$. The solution set of the inequality $\frac{(x+1)f(x+1)}{4} < \frac{f(2)}{x+1}$ is ______.

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