
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 $f(x)=2x^{3}+ax^{2}+bx+1$, let $f'(x)$ denote its derivative. If the graph of the function $y=f'(x)$ is symmetric about the line $x=-\frac{1}{2}$, and $f'(1)=0$:

(1) Find the values of the real numbers $a$ and $b$.
(2) Find the extreme values of the function $f(x)$.

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