
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
The competition with $n (n \geqslant 2)$ contestants lasts for $k$ days. Each day, the scores of the contestants are exactly $1, 2, \cdots, n$ (with no two contestants having the same score). After $k$ days, the total score of each contestant is 26. Find all possible values of $(n, k)$.

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