
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 $f(x)=x^{3}+ax^{2}+bx+c$ has extreme values at $x=1$ and $x=-\frac{2}{3}$.  
(1) Find the values of $a$ and $b$;  
(2) If $f(-1)=\frac{3}{2}$, determine the intervals of monotonicity and the extreme values of $f(x)$.

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