
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
Two cones, A and B, have equal slant heights. The sum of the central angles of their unfolded side views is $\frac{{3π}}{2}$. The surface areas are $S_A$ and $S_B$, and the volumes are $V_A$ and $V_B$. If $\frac{{S_A}}{{S_B}}=2$, then $\frac{{V_A}}{{V_B}}=\_\_\_\_\_\_$.

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