
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
The graph of the function $f(x) = ax^3 + bx^2 + cx + d$ intersects the y-axis at point P, and the equation of the tangent line to the graph at point P is $12x - y - 4 = 0$. Given that the function $f(x)$ has an extremum of 0 at $x=2$.

(1) Find the explicit formula for the function $f(x)$;
(2) Determine the intervals where the function $f(x)$ is monotonically increasing.

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