
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 $y = ax^3 + bx^2$, it has a local maximum value of 3 when $x = 1$.
(1) Find the expression for the function.
(2) State its intervals of monotonicity.
(3) Find the maximum and minimum values of this function on the interval \[-2, 2\].

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