
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
Through every three vertices of a cube, located at the ends of each trio of edges meeting at one vertex, a plane is drawn. Find the volume of the solid bounded by these planes if the edge length of the cube is $a$.

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