
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
$EFGH$ is a rectangle that forms the base of pyramid $Q$ with dimensions $EF = 9$ and $FG = 15$. The height of the pyramid, $VQ$, is $30$. A plane, parallel to the base $EFGH$, slices through the pyramid creating a frustum $G$ and a smaller pyramid $Q'$. If the volume of $Q$ is nine times that of $Q'$, find the distance $YQ$ where $Y$ is the center of the circumsphere of frustum $G$ and $Q$ is the apex of the pyramid.

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