
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
Three concentric circles with the same center \( O \) have areas \( 2 \pi, 3 \pi, \) and \( 4 \pi \). From a point \( A \) on the largest circle, tangent lines are drawn to points \( B \) on the middle circle and \( C \) on the smallest circle. If \( B \) and \( C \) are on the same side of \( OA \), find the exact value of \( \angle BAC \).

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