
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
In the equation $w^3 + x^3 + y^3 = kz^3$, where $w$, $x$, $y$, and $z$ are distinct, consecutive positive integers and $k$ is a positive integer factor, find the smallest possible value of $z$ that satisfies the equation for $k = 2$.

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