
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 min{p, q} = $$\begin{cases} p & (p \leq q) \\ q & (p > q)\end{cases}$$, if the function $f(x) = \min\{3+\log_{\frac{1}{4}}x, \log_{2}x\}$  
(1) Write the piecewise function of $f(x)$;  
(2) Solve the solution set of the inequality $0 < f(x) < 2$.

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