
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
Solve the inequality:

\[
\frac{\left(\log _{4}(6-x)-\log _{4} 1\right)(|x-5|-|x-1|)}{\left(3^{x}-9\right)\left(3^{x}-3\right)\left(\log _{3} x-\log _{3} 1\right)} \leq 0
\]

with the domain of definition: \(x > 0, 6 - x > 0, x \neq 1, x \neq 2 \Rightarrow x \in (0, 1) \cup (1, 2) \cup (2, 6)\).

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