
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 $f(x)=x^{3}+f'( \frac {2}{3})x^{2}-x+c$ (where $f'( \frac {2}{3})$ is the derivative of $f(x)$ at the point $x= \frac {2}{3}$, and $c$ is a constant).  
(1) Find the value of $f'( \frac {2}{3})$;  
(2) Determine the intervals of monotonicity for the function $f(x)$;  
(3) Let the function $g(x)=[f(x)-x^{3}]\cdot e^{x}$. If the function $g(x)$ is monotonically increasing on the interval $[-3,2]$, find the range of values for the real number $c$.

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