
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 circumscribed circle $\Omega$ is drawn around an isosceles acute triangle $ADE$ with base $AD$. The distance from the midpoint of arc $DE$, which does not contain point $A$, to side $DE$ is 5, and the distance from the midpoint of arc $AD$, which does not contain point $E$, to side $AD$ is $\frac{1}{3}$. Find the radius of circle $\Omega$ and the area of triangle $ADE$.

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