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

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