
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 radius of the arc of sector \(AOB\) is \(R\), and the central angle \(AOB\) is \(\alpha\). An equilateral triangle is inscribed in this sector such that one of its vertices coincides with the midpoint of the arc \(AB\), and the other two vertices lie on radii \(OA\) and \(OB\), respectively. Find the sides of the triangle.

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