
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 image of a cube, construct a line segment determining the distance between two skew diagonals of two adjacent faces of the cube. Calculate this distance if the edge length of the cube is \(a\).

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