
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 $EFGH$ be a rectangle in space, where $EF = 12$ and $FG = 4$. On the Z-axis perpendicular to the plane containing $EFGH$, let there be points $E'$, $F'$, $G'$, and $H'$ such that $EE' = 20$, $FF' = 12$, $GG' = 30$, and $HH' = 24$. Suppose $P$ and $Q$ are the midpoints of segments $E'G'$ and $F'H'$, respectively. Determine the length of $PQ$.
**A)** 4
**B)** 6
**C)** 7
**D)** 8
**E)** 10

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