
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
Let $ABCD$ be a rectangle with $AB = 15$ and $BC = 20$, forming the base of pyramid $P$ with a height of $30$. A plane parallel to $ABCD$ cuts through $P$ creating a smaller pyramid $P'$ beneath the plane and a frustum $F$ above it. Considering $Q$ as the center of the base of $P'$ and $R$ as the apex of $P$, find $QR$ if the volume of $P$ is three times that of $P'$.

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