
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
A triangle ABC with  $\angle A = 60^o$  is given. Points  $M$  and  $N$  on  $AB$  and  $AC$  respectively are such that the circumcenter of  $ABC$  bisects segment  $MN$ . Find the ratio  $AN:MB$ .


by E.Bakaev

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