
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 is played amongst \( n > 1 \) players over \( d \) days. Each day one player gets a score of 1, another a score of 2, and so on up to \( n \). At the end of the competition, each player has a total score of 26. Find all possible values for \( (n, d) \).

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