
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
In an acute-angled triangle \( \mathrm{ABC} \), angle \( \mathrm{B} = 75^\circ \). A point \( K \) is chosen on side \( \mathrm{AC} \). Circles are circumscribed around triangles \( \mathrm{ABK} \) and \( \mathrm{CBK} \), with centers \( \mathrm{O}_1 \) and \( \mathrm{O}_2 \) respectively. Find the radius of the circumcircle of triangle \( \mathrm{ABC} \) if the smallest possible length of segment \( \mathrm{O}_1 \mathrm{O}_2 \) is 2 cm.

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