
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 us consider a regular octagon $ABCDEFGH$ where each side of the octagon has a length of $5$ units. Suppose lines $\overline{AE}$ and $\overline{CG}$ intersect at point $M$. Calculate the area of the quadrilateral $ABCM$.
A) \(12.5\sqrt{2}\)
B) \(20\sqrt{2}\)
C) \(22.5\sqrt{2}\)
D) \(25\sqrt{2}\)

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