
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
Acute triangle \( A B C \) has circumcenter \( O \). The bisector of \( \angle A B C \) and the altitude from \( C \) to side \( A B \) intersect at \( X \). Suppose that there is a circle passing through \( B, O, X, \) and \( C \). If \( \angle B A C = n^{\circ} \), where \( n \) is a positive integer, compute the largest possible value of \( n \).

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