
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 $ABCD$ be a parallelogram in the $xy$-plane with $A(0,0,0)$, $B(1,2,0)$, $C(4,2,0)$, and $D(3,0,0)$. Points $A'$, $B'$, $C'$, and $D'$ are directly above $A$, $B$, $C$, and $D$ in the $z$-direction at distances of $5$, $3$, $9$, and $7$ units respectively. Let $M$ and $N$ be the midpoints of segments $A'C'$ and $B'D'$. Calculate the length of segment $MN$.

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