
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 $f(x)$ is a monotonically increasing function defined on $(0,+\infty)$, and for any $x\in (0,+\infty)$, it satisfies $f\left[ f(x)-\log_{2}x \right]=3$. Find the interval containing the zero point of the function $y=f(x)-f'(x)-2$ (where $f'(x)$ is the derivative of $f(x)$).

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