
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 the function $f(x) = \ln{\frac{x}{2}} - ax + \frac{b}{x}$ ($a, b > 0$), for any $x > 0$, we have $f(x) + f(\frac{4}{x}) = 0$.
(1) Discuss the monotonicity of $f(x)$;
(2) When $f(x)$ has three distinct zeros, find the range of values for the real number $a$.

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