
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
Two circumferences of radius  $1$  that do not intersect,  $c_1$  and  $c_2$ , are placed inside an angle whose vertex is  $O$ .  $c_1$  is tangent to one of the rays of the angle, while  $c_2$  is tangent to the other ray. One of the common internal tangents of  $c_1$  and  $c_2$  passes through  $O$ , and the other one intersects the rays of the angle at points  $A$  and  $B$ , with  $AO=BO$ . Find the distance of point  $A$  to the line  $OB$ .

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