
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
Let \( P, Q, R, S \) be four points inside the tetrahedron \( A-BCD \), where \( Q, R, S, P \) are the midpoints of \( PA, QB, RC, SD \) respectively. If \( V_{P-ABC} \) denotes the volume of the tetrahedron \( P-ABC \), and similarly for the others, then what is the ratio \( V_{P-ABC} : V_{P-BCD} : V_{P-DAB} : V_{P-DAC} = \) ?

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