
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
The parabola \( y = ax^2 + bx + c \) has its vertex at \( (4, 2) \) and the point \( (2, 0) \) lies on the parabola. Determine the value of \( abc \).

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