
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 quadratic equation $6x^2 - 8x + 2k = 0$ that has real roots, find the value of $k$ such that the product of the roots is maximum.
A) $\frac{64}{48}$
B) $\frac{8}{3}$
C) $\frac{4}{9}$
D) $\frac{4}{3}$
E) $-\frac{4}{3}$

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