
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 area of triangle \( ABC \) is \( 2\sqrt{3} - 3 \), and angle \( BAC \) is \( 60^\circ \). The radius of the circle touching side \( BC \) and the extensions of sides \( AB \) and \( AC \) is 1. Find the angles \( ABC \) and \( ACB \) of the given triangle.

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