
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 triangle \( \triangle ABC \), let \( a = BC \), \( b = CA \), and \( c = AB \). Given that \( a^{2} + b^{2} = 6 \) and \( \cos(A - B) \cos C = \frac{2}{3} \), find the circumradius of \( \triangle ABC \).

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