
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 $f(x) = ax^3 + bx^2$, and the tangent line to $f(x)$ at point $P(-1, -2)$ is perpendicular to the line $3x - y = 0$. (1) Find the values of $a$ and $b$. (2) If $f(x)$ is monotonic on the interval $[0, m]$, determine the range of values for $m$.

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