
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
Given $WXYZ$ be a rectangle in space with vertices at $W(0,0,0)$, $X(0,5,0)$, $Y(6,5,0)$, and $Z(6,0,0)$, $WW' = 10$, $XX' = 20$, $YY' = 10$, and $ZZ' = 20$, find the length of the line segment $PQ$, where $P$ and $Q$ are the midpoints of $W'Y'$ and $X'Z'$ respectively.

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