
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 the $xy$-plane with $E(0,0,0)$, $F(2,0,0)$, $G(2,3,0)$, and $H(0,3,0)$. Rays $\overrightarrow{EE^\prime}$, $\overrightarrow{FF^\prime}$, $\overrightarrow{GG^\prime}$, and $\overrightarrow{HH^\prime}$ are parallel to the $z$-axis, extending in the positive $z$-direction. Let $EE' = 12$, $FF' = 16$, $GG' = 20$, and $HH' = 24$. Let $P$ and $Q$ be the midpoints of $E^{\prime}G^{\prime}$ and $F^{\prime}H^{\prime}$ respectively. Determine the length of $PQ$.
A) 2
B) 3
C) 4
D) 5

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