
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 $f(x) = \begin{cases} 2^{-x}, & x \leqslant 1 \\ \log_{3} \frac{x}{3} \cdot \log_{3} \frac{x}{9}, & x > 1 \end{cases}$,

(1) Find the value of $f(\log_{2} \frac{3}{2})$;

(2) Find the minimum value of $f(x)$.

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