
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
The bases of a parallelepiped are squares with side length \( b \), and all the lateral faces are rhombi. One of the vertices of the upper base is equidistant from all the vertices of the lower base. Find the volume of the parallelepiped.

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