
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 functions $g(x)=e^{x}-ex-1$, $h(x)=a\sin x-ex$.

    (1) Find the intervals of monotonicity for $g(x)$;

    (2) If $g(x) \geqslant h(x)$ holds for all $x \in [0,1]$, find the range of values for $a$.

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