
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 $f(x) = mx^3 + nx^2$ ($m, n \in \mathbb{R}, m \neq 0$), the graph of the function $y = f(x)$ has a tangent line at the point $(2, f(2))$ that is parallel to the x-axis.  
(1) Express $n$ as an algebraic expression in terms of $m$;  
(2) Find the intervals where the function $f(x)$ is increasing.

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