
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 the function $f(x)=ax^3+bx^2+cx+d$ (where $a \ne 0$) passes through the origin and $f'(1)=0$, and $f(x)$ attains a local maximum of 2 at $x=-1$,
(1) Determine the expression for the function $y=f(x)$;
(2) If for any $x \in [-2, 4]$, it holds that $f(x) \geq f'(x) + 6x + m$, find the maximum value of $m$.

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