
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
A circle with diameter \(AB\) intersects segments \(AC\) and \(BC\) at points \(M\) and \(N\), respectively. The length of segment \(MN\) is equal to the radius of the circle. Find the area of quadrilateral \(ABNM\), given that \(AC = 12\) and \(BC = 8\).

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