
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 two sides and the included angle of a spherical triangle: \( a = 97^{\circ} 30' 20'' \), \( b = 55^{\circ} 12' 10'' \), \( \gamma = 39^{\circ} 58' \). Find the opposite two angles and the third side (\( \alpha, \beta \), and \( c \)).

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