
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 the regular tetrahedron \( P-ABC \), points \( D \), \( E \), and \( F \) lie on edges \( PA \), \( PB \), and \( PC \) respectively. If \( PE \neq PF \), and \( DE = DF = \sqrt{7} \), \( EF = 2 \), find the volume of the tetrahedron \( P-DEF \).

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