
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 three mutually perpendicular lines, the distance between any two of which is equal to \(a\). Find the volume of the parallelepiped whose space diagonal lies along one of these lines, and the diagonals of two adjacent faces lie along the other two lines.

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