
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 an even function $f(x)$ with the domain $[-4, 0) \cup (0, 4]$, if for $x \in (0, 4]$ we have $f(x) = \log_{2}x$,

  (1) Find the explicit formula for the function on its domain $[-4, 0) \cup (0, 4]$;

  (2) Find the solution set of the inequality $xf(x) < 0$.

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