
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
Let  $ m, n \geq 1$  be two coprime integers and let also  $ s$  an arbitrary integer. Determine the number of subsets  $ A$  of   $ \{1, 2, ..., m \plus{} n \minus{} 1\}$  such that  $ |A| \equal{} m$  and  $ \sum_{x \in A} x \equiv s \pmod{n}$ .

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