
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
$ABCD$ is a rectangle acting as the base of pyramid $P$, with dimensions $AB = 15$ and $BC = 20$. Pyramid $P$ has a height of $30$. A plane parallel to base $ABCD$ slices through $P$, forming a frustum $F$ and a smaller pyramid at the top, $P'$. If the volume of $P$ is nine times that of $P'$, determine the height from the top $T$ of $P$ to plane slicing $P'$.

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