
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
In a competition with \( n (\geqslant 2) \) participants lasting \( k \) days, each participant scores exactly \( 1, 2, \cdots, n \) points each day (no two participants have the same score on the same day). After \( k \) days, the total score of each participant is 26. Determine all possible values of \( (n, k) \).

(22nd Canadian Mathematical Competition, 1990)

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