
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 $f(x)=\frac{1}{3}x^{3}-\frac{1}{2}x^{2}-2ax$,
(I) Find the extreme values of $f(x)$ when $a=1$;
(II) Determine the range of $a$ values for which $f(x)$ is strictly increasing on $(\frac{2}{3},+\infty)$.

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