
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 a regular tetrahedron \( ABCD \) with edge length \( a \), points \( A_1 \), \( B_1 \), \( C_1 \), and \( D_1 \) are chosen in the planes \( BCD \), \( CDA \), \( DAB \), and \( ABC \), respectively, such that the line \( A_1B_1 \) is perpendicular to the plane \( BCD \), the line \( B_1C_1 \) is perpendicular to the plane \( CDA \), the line \( C_1D_1 \) is perpendicular to the plane \( DAB \), and the line \( D_1A_1 \) is perpendicular to the plane \( ABC \). Find the volume of the tetrahedron \( A_1B_1C_1D_1 \).

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