
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
Let $f(x)$ be a monotonic function defined on the domain $(0,+\infty)$, and for any $x \in (0,+\infty)$, it holds that $f[f(x)-\log_{2}x]=6$. If $x_{0}$ is a solution to the equation $f(x)-f'(x)=4$, and $x_{0} \in (a,a+1) (a \in \mathbb{N}^{*})$, then the real number $a=$ ______.

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