
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 and let $\overline{DM}$ be a segment perpendicular to the plane of $ABCD$. Suppose $\overline{DM}$ has integer length, and the lengths of $\overline{MA},\overline{MB},$ and $\overline{MC}$ are consecutive even positive integers. What is the volume of the pyramid $MABCD$?
A) $8\sqrt{3}$
B) $12\sqrt{3}$
C) $16\sqrt{3}$
D) $24\sqrt{3}$

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