
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  $ k,m,n$  be integers such that  $ 1 < n \leq m \minus{} 1 \leq k.$  Determine the maximum size of a subset  $ S$  of the set  $ \{1,2,3, \ldots, k\minus{}1,k\}$  such that no  $ n$  distinct elements of  $ S$  add up to  $ m.$ 

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