
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
Define a monotonic function $f(x)$ on $(0, +\infty)$. For any $x \in (0, +\infty)$, the equation $f[f(x) - \log_{2}x] = 3$ holds. If the solution to the equation $f(x) - f'(x) = 2$ is in the interval $(k, k+1)$ ($k \in \mathbb{Z}$), then $k = \_\_\_\_\_\_$.

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