
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
Let $f(x) = -\frac{1}{3}x^3 + \frac{1}{2}x^2 + 2ax$.
(1) If $f(x)$ has a strictly increasing interval on $(\frac{2}{3}, +\infty)$, find the range of values for $a$.
(2) When $a=1$, find the maximum and minimum values of $f(x)$ on the interval $[1,4]$.

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