
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 $f(x)=ae^{x}+2e^{-x}+(a-2)x$ ($a\in \mathbb{R}$, $e$ is the base of the natural logarithm).

(1) Discuss the monotonicity of $f(x)$.

(2) When $x \gt 0$, $f(x)\geqslant (a+2)\cos x$, find the range of values for $a$.

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