
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 inscribed circle \( O \) of triangle \( \triangle ABC \) is tangent to \( BC \) at point \( D \), and the radius of the inscribed circle is \( r \). If \( AD = 2\sqrt{3} \), \( DB = \sqrt{3} \), and \( \angle A > 60^\circ \), what is the range of values for \( r \)?

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