
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
Given that $P, Q, R, S$ are four points inside the triangular pyramid $A-BCD$, and $Q, R, S, P$ are the midpoints of $PA, QB, RC$, and $SD$ respectively, find the ratio $V_{P-AHC} : V_{P-1XD} : V_{r-(DA} : V_{P-DAB}$.

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