
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 rectangle in space, with $AB = 2$ and $BC = 1$, and let vectors $\overrightarrow{AA'}$, $\overrightarrow{BB'}$, $\overrightarrow{CC'}$, and $\overrightarrow{DD'}$ extend identically from vertices in the positive z-direction, where $AA' = 6$, $BB' = 3$, $CC' = 12$, and $DD' = 15$. Find the distance between $N$, the midpoint of $B'D'$, and $P$, the midpoint of $BD$.
A) 4
B) 6
C) 8
D) 9
E) 10

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