
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 $$f(x)= \begin{cases} -2, & 0<x<1 \\ 1, & x\geq 1 \end{cases}$$, then the solution set of the inequality $$\log_{2}x-(\log_{ \frac {1}{4}}4x-1)f(\log_{3}x+1) \leq 5$$ is \_\_\_\_\_\_.

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