
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 every $x \in (0, +\infty)$, it satisfies $f[f(x) - \log_3{x}] = 4$. If $x_0$ is a solution of the equation $f(x) - 2f'(x) = 3$ and $x_0 \in (a, a+1)$ where $a \in \mathbb{N}^*$, find the value of the real number $a$.

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