
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 $f(x)=(ax^2+2x-2)e^x$, where $e$ is the base of the natural logarithm, and $a\in R$.

(1) If $a=1$, find the equation of the tangent line to the curve $f(x)$ at the point $(1,f(1))$;

(2) If $a < 0$, find the monotonic intervals of $f(x)$;

(3) If $a=-2$, the graph of the function $f(x)$ intersects the graph of the function $g(x)=\frac{1}{3}x^3+\frac{1}{2}x^2+m$ at 3 distinct points. Find the range of values of the real number $m$.

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