
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
In a 3-dimensional coordinate system, consider parallelogram $ABCD$ where $A = (0, 0, 0)$, $B = (4, 0, 0)$, $C = (6, 2, 0)$, and $D = (2, 2, 0)$. Rays are extended from these points in the $z$-direction, such that $AA' = 12$, $BB' = 10$, $CC' = 20$, and $DD' = 24$. Let $M$ and $N$ be the midpoints of $A'C'$ and $B'D'$ respectively. Find the value of $MN$.
A) 0 
B) 1 
C) 2
D) 3
E) 4

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