
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 $f(x)=- \frac{1}{3}x^{3}+ \frac{1}{2}x^{2}+2ax$, when $0 < a < 2$, the minimum value of $f(x)$ on $x \in [1,4]$ is $- \frac{16}{3}$. Determine the maximum value of $f(x)$ on this interval.

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