
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
There are $n (\geqslant 2)$ contestants participating in a competition spanning $k$ days. Each day, a contestant can score $1, 2, 3, \cdots, n$ points, with no two contestants achieving the same score on any given day. After $k$ days of competition, it is observed that each contestant's total score is 26 points. Determine all possible pairs $(n, k)$.

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