
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
In a circle with center \( O \) and radius \( 2r \), chord \( AB \) is drawn such that \( AB = 2r \). From \( O \), a perpendicular to \( AB \) meets \( AB \) at \( M \). From \( M \) a perpendicular to \( OA \) meets \( OA \) at \( D \). Determine the area of triangle \( MDA \) in terms of \( r \).

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