
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
The function $f(x)=e^{x}(x^{2}-ax-a)$.  
$(1)$ If $x=1$ is a critical point of the function $f(x)$, find the value of $a$ and determine whether $x=1$ is a local maximum or minimum point.  
$(2)$ Find the intervals where the function $f(x)$ is monotonic.

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