
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
Points \( A, B, C, D \) are the centers of the circles inscribed in the faces \( PQS, PRS, QRS, \) and \( PQR \) of the tetrahedron \( PQRS \). It is known that \( PQ = RS = 7 \), \( PR = QS = 8 \), \( PS = QR = 9 \). Find the volume of the tetrahedron \( ABCD \). If necessary, round the answer to two decimal places.

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