
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
21) Given that $a \in \mathbb{R}$, the function is defined as $f(x) = ax^3 - 3x^2$.
(1) If $x = 2$ is an extreme point of the function $y = f(x)$, find the value of the real number $a$;
(2) If the function $g(x) = e^x f(x)$ is monotonically decreasing on the interval $[0, 2]$, find the range of values for the real number $a$.

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