
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
Suppose that $f(x)$ is a monotonic function defined on $(0,+\infty)$, and for any $x\in(0,+\infty)$, there is $f[f(x)-\log_{3}x]=4$. If $x_{0}$ is a solution to the equation $f(x)-2f'(x)=3$, 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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