
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
Let \( f(x) \) be a monotonic function defined on the interval \( (0, +\infty) \). For any \( x > 0 \), it holds that 
\[ f(x) > -\frac{4}{x}, \]
and
\[ f\left(f(x) + \frac{4}{x}\right) = 3. \]

Find \( f(8) \).

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