
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 $f(x) = x^3 + ax^2 + bx + c$, it takes extreme values at $x = 1$ and $x = -\frac{2}{3}$.

(1) Find the values of $a$ and $b$.
(2) If $f(-1) = \frac{3}{2}$, find the monotonic intervals and extreme values of the function $f(x)$.

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