
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
a) \(\sin ^{2} \alpha + \sin ^{2} \beta + \sin ^{2} \gamma = \left(p^{2}-r^{2}-4rR\right) / 2R^{2}\).

b) \(4R^{2} \cos \alpha \cos \beta \cos \gamma = p^{2} - (2R + r)^{2}\).

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