
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 monotonous function defined on the domain $(0, +\infty)$. For any $x \in (0, +\infty)$, it satisfies $f\left[f(x) - \log_{2}x\right] = 6$. If $x_0$ is a solution to the equation $f(x) - f'(x) = 4$ and $x_0 \in (a, a + 1)$ where $a \in \mathbb{N}^{*}$, find the value of $a$.

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