
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 $f(x) = (x^2 + ax - 2a - 3)e^x$, which has an extremum at $x = 2$,
(1) Find the value of $a$;
(2) Find the maximum and minimum values of $f(x)$ in the interval $\left[\frac {3}{2}, 3\right]$.

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