
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 functions $f(x)=e^{x}-ax$ and $g(x)=2-\sin x-\cos x$.  
$(1)$ Discuss the monotonic intervals of the function $f(x)$.  
$(2)$ If $f(x)\geq g(x)$ always holds in $[-\frac{π}{2},\frac{π}{4}]$, find the set of real numbers for $a$.

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