
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
Solve the triangle if a side $a$, the angle opposite to it $\alpha$, and the difference between the other two sides $b - c$ are given. $\left(a = 631.28 \, \text{dm}, \, \alpha = 63^\circ 35' 30'', \, b - c = 373 \, \text{dm}\right)$.

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