
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
Given triangle  $ ABC$ . Point  $ O$  is the center of the excircle touching the side  $ BC$ . Point  $ O_1$  is the reflection of  $ O$  in  $ BC$ . Determine angle  $ A$  if  $ O_1$  lies on the circumcircle of  $ ABC$ .

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