
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 $f(x) = x^3 - 3ax + b$ $(a \neq 0)$. If the curve $y = f(x)$ is tangent to the line $y = 8$ at the point $(2, f(2))$, find the value of the product $ab$.

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