
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 a cube \( A B C D A_{1} B_{1} C_{1} D_{1} \), what is the smaller part of the volume separated by the plane that passes through the midpoints of the edges \( A B, B B_{1} \), and \( A_{1} D_{1} \)?

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