
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 $\Omega$ is circumscribed around an isosceles acute triangle $F K T$ with base $K T$. Point $M$ is the midpoint of the arc $F T$ that does not contain point $K$. It is known that the distances from point $M$ to the lines $K T$ and $F T$ are $\frac{9}{5}$ and 1, respectively. Find the radius of the circle $\Omega$ and the area of the triangle $F K T$.

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