
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 such that the length of $AB$ is $r\sqrt{2}$ units. From $O$, a perpendicular to $AB$ meets $AB$ at $M$. From $M$ a perpendicular to $OA$ meets $OA$ at $D$. Find the area of triangle $MDA$, in terms of $r$.
A) $\frac{r^2}{2}$
B) $\frac{r^2}{4}$
C) $\frac{r^2}{8}$
D) $\frac{r^2}{16}$

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