
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 $f(x) = - \frac{n}{3}x^3 - \frac{1}{2}x^2 + 2mx$,
(1) If $m = 3$ and $n = 1$, find the extreme values of $f(x)$;
(2) If $n = -1$ and $-2 < m < 0$, and the maximum value of $f(x)$ in the interval $[1, 4]$ is $\frac{16}{3}$, find the minimum value of $f(x)$ in this interval.

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