
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 that $a \in \mathbb{R}$, and the function $f(x) = ax^3 - 3x^2$.

1. Find the monotonic intervals of the function $f(x)$.
2. Given that $g(x) = f(x) + f'(x)$, and there exists $x \in [1, 3]$ such that $g(x) \leqslant 0$, find the range of values for the real number $a$.

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