
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 $f(x)=mx^3+nx^2$ where $m, n \in \mathbb{R}, m \neq 0$, the tangent to the graph of $y=f(x)$ at the point $(2, f(2))$ is parallel to the x-axis.

1. Express $n$ algebraically in terms of $m$.
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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