
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
The angles of a triangle are $\alpha=74^\circ 15' 46''$, $\beta=36^\circ 9' 24''$, and $\gamma=69^\circ 34' 50''$. The radius of the circumscribed circle around the triangle is $r = 2$ dm. How large is the area of the triangle formed by the tangents drawn to the circle at the vertices of the original triangle?

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