
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]


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Given that \( f(x) \) is a monotonic function defined on the interval \( (0,+\infty) \), and for \( \forall x \in (0,+\infty) \), it holds that \( f[f(x)-\ln x]=e+1 \), determine the number of zeros of the function \( g(x)=f(x)-f'(x) \).

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