
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 the acute-angled triangle  $ABC$  the angle $ \angle B = 30^o$ , point  $H$  is the intersection point of its altitudes. Denote by  $O_1, O_2$  the centers of circles inscribed in triangles   $ABH ,CBH$   respectively. Find the degree of the angle between the lines  $AO_2$  and  $CO_1$ .

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