
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 $f(x) = ax^3 + bx^2$, its graph passes through the point $M(1, 4)$, and the tangent to the curve at point $M$ is perpendicular to the line $x + 9y = 0$.  
(1) Find the values of the real numbers $a$ and $b$.  
(2) If the function $f(x)$ is monotonically increasing on the interval $[m, m+1]$, find the range of values for $m$.

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