
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) = 2x³ + ax² + bx + 1, its derivative is f′(x). If the vertex of the graph of the function y = f′(x) has an x-coordinate of -1/2, and f′(1) = 0, find the value of a + b.

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