
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 that $x$ satisfies the inequality $\log_{\frac{1}{2}} x^2 \geq \log_{\frac{1}{2}} (3x-2)$, and the function $f(x) = (\log_{2} \frac{x}{4})(\log_{2} \frac{x}{2})$.
- (I) Find the range of values for $x$.
- (II) Find the range of values for $f(x)$.

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