
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 a real number $x$ satisfying $3^{2x-4} - \frac{10}{3} \cdot 3^{x-1} + 9 \leq 0$, and $f(x) = \log_{2} \frac{x}{2} \cdot \log_{2} \frac{\sqrt{x}}{2}$.
(1) Find the range of values for the real number $x$;
(2) Find the maximum and minimum values of $f(x)$, and the corresponding values of $x$.

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