
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
Let  $ABC$  is a triangle with  $\angle BAC=\frac{\pi}{6}$  and the circumradius equal to 1. If  $X$  is a point inside or in its boundary let  $m(X)=\min(AX,BX,CX).$  Find all the angles of this triangle if  $\max(m(X))=\frac{\sqrt{3}}{3}.$ 

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