
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 $f(x) = ax^3 + x^2$ $(a \in \mathbb{R})$ has an extremum at $x = -\frac{4}{3}$.
1. Determine the value of $a$;
2. If $g(x) = f(x)e^x$, discuss the monotonicity of $g(x)$.

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