
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
A rectangular base $ABCD$ with dimensions $AB = 15$ and $BC = 20$ forms the base of pyramid $Q$, which has a height of $30$. A plane parallel to the base cuts through $Q$, resulting in a frustum $G$ and a smaller pyramid $Q'$. Let $Y$ be the center of the circumsphere of frustum $G$, and $Z$ be the apex of $Q$. If the volume of $Q$ is eight times that of $Q'$, determine the length of $YZ$. Express your answer in simplest form.

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