
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
Tetrahedron \(PQRS\) has \(PQ = 6\), \(PR = 4\), \(PS = 5\), \(QR = 5\), \(QS = 3\), and \(RS = \frac{15}{4}\sqrt{2}\). Calculate the volume of the tetrahedron.
**A)** \(3\sqrt{2}\)  
**B)** \(2\sqrt{5}\)  
**C)** \(\frac{24}{5}\)  
**D)** \(3\sqrt{3}\)  
**E)** \(\frac{24}{5}\sqrt{2}\)

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