
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
Square \( MNPQ \) is inside square \( ABCD \) such that each side of \( MNPQ \) extends to pass through a vertex of \( ABCD \). The outer square \( ABCD \) has a side length of \( \sqrt{72} \) and \( BM = 2 \). A circle with radius \( 1 \) centered at \( M \) touches the side \( AB \). What is the area of the inner square \( MNPQ \)?
A) 12
B) 14
C) 16
D) 18
E) 20

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