
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
Consider a square-based pyramid (with base vertices $A, B, C, D$) with equal side edges, and let the apex be $E$. Let $P$ be the point that divides the side edge $A E$ in a ratio of 3:1, such that $E P : P A = 3$, and let $Q$ be the midpoint of the side edge $C E$. In what ratio does the plane passing through points $D, P$, and $Q$ divide the side edge $B E$?

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