
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
Given the function $f(x)=e^{x}-ax-2$,
(1) Find the monotonic intervals of $f(x)$;
(2) If $a=1$, $k$ is an integer, and $\frac{k-x}{x+1}f'(x) < 1$ always holds when $x > 0$, where $f'(x)$ is the derivative of $f(x)$, find the maximum value of $k$.

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