
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 a rectangular box measures $x \times y \times z$, where $x$, $y$, and $z$ are integers and $1 \leq x \leq y \leq z$, determine the number of ordered triples $(x, y, z)$ such that the sum of the volume and surface area equals twice the surface area plus 12.

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