
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
A competition involving  $n\ge 2$  players was held over  $k$  days. In each day, the players received scores of  $1,2,3,\ldots , n$  points with no players receiving the same score. At the end of the  $k$  days, it was found that each player had exactly  $26$  points in total. Determine all pairs  $(n,k)$  for which this is possible.

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