
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 $WXYZ$ be a rectangle in the $xy$-plane with $W = (0,0,0)$, $X = (2,0,0)$, $Y = (2,3,0)$, and $Z = (0,3,0)$. Vertices $W'$, $X'$, $Y'$, and $Z'$ extend straight up from $W$, $X$, $Y$, and $Z$, respectively, with $WW' = 12$, $XX' = 16$, $YY' = 24$, and $ZZ' = 12$. Let $P$ and $Q$ be the midpoints of $W'Y'$ and $X'Z'$, respectively. Find the distance $PQ$.

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