
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 $(0,+\infty)$. Let $f'(x)$ be its derivative. For $x > 0$ and $x \neq 1$, $\frac{2f(x)+xf'(x)}{x-1} > 0$. The slope of the tangent line to the curve $y=f(x)$ at $x=1$ is $-\frac{3}{4}$. Find $f(1)$.

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