
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
Let $f(x) = e^{x} + a\sin x - ax^{2} - (1+a)x$.  
$(1)$ When $a \leq 0$, discuss the monotonicity of $f(x)$.  
$(2)$ If $f(x)$ is monotonically increasing on $\mathbb{R}$, find $a$.

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