
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
$S-ABCD$ is a regular quadrilateral pyramid. $P$ and $Q$ are the midpoints of $SB$ and $SD$, respectively. The plane passing through points $A$, $P$, and $Q$ divides $S-ABCD$ into two parts with volumes $V_1$ and $V_2$ ($V_1 < V_2$). Find the ratio $\frac{V_2}{V_1}$.

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