
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 $r$, chord $AB$ is drawn with length equal to $\sqrt{2}r$ units. From $O$, a perpendicular to $AB$ meets $AB$ at point $M$. From $M$, a perpendicular to $OA$ meets $OA$ at point $D$. What is the area of triangle $MDA$ expressed in terms of $r$?
A) $\frac{3r^2}{16}$
B) $\frac{\pi r^2}{16}$
C) $\frac{r^2 \sqrt{3}}{8}$
D) $\frac{r^2}{4\sqrt{3}}$
E) $\frac{r^2\sqrt{6}}{48}$

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