
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 circle inscribed in triangle \(ABC\) touches side \(BC\) at point \(D\), with \(BD = 5\). Find the radius of this circle and the area of triangle \(ABC\), given that angle \(A\) is \(60^\circ\) and the radius of the circumscribed circle around triangle \(ABC\) is \(\frac{7}{\sqrt{3}}\).

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