
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 $f(x) = x^3 + ax^2 + bx + c$, and $g(x) = 12x - 4$. If $f(-1) = 0$, and the tangent line to the graph of $f(x)$ at the point $(1, f(1))$ is $y = g(x)$.

(1) Find the values of the real numbers $a$, $b$, and $c$;  
(2) Determine the intervals of monotonicity for the function $h(x) = f(x) - g(x)$.

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