
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 that \(\overline{DM}\) has integer length and the lengths of \( \overline{MA}, \overline{MC}, \overline{MB}\) are consecutive even positive integers (in this order). What is the volume of pyramid \(MABCD\)?
A) \( \frac{96}{3} \sqrt{6} \)
B) \( \frac{128}{3} \sqrt{6} \)
C) \( \frac{128}{3} \sqrt{8} \)
D) \( \frac{128}{3} \sqrt{5} \)

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