
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 the function $f(x) = 2x^3 + ax^2 + bx + m$ have a derivative denoted as $f'(x)$. 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) If the function $f(x)$ has exactly three zeros, determine the range of the real number $m$.

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