
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 2017×2017 table is filled with non-zero digits. Among the 4034 numbers, whose decimal representations are identical to the rows and columns of this table read left to right and top to bottom, all but one are divisible by the prime number \( p \), and the remaining number is not divisible by \( p \). Find all possible values of \( p \).

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