
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
A rectangular box has dimensions \( a \times b \times c \), where \( a \), \( b \), and \( c \) are integers with \( 2 \leq a \leq b \leq c \). The volume of the box is twice the surface area. Determine the number of ordered triples \( (a, b, c) \) that satisfy these conditions.

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