
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 the function $y=f(x)$ is an even function defined on $[-4,4]$, and $f(x)= \begin{cases} 3^{x}-9,&0\leqslant x\leqslant 4 \\ g(x),&-4\leqslant x < 0 \end{cases}$, express the solution set of the inequality $(1-2x)g(\log_{2}x) < 0$ in interval notation.

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