
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
Given natural numbers $P$ and $P'$ such that $P = P'+10$ and both are divisible by 10 (hence $P$ and $P'$ leave a remainder of 0 when divided by 10). When $P^2 - P'^2$ and $0$ are divided by $D=10$, the remainders are $r$ and $r'$ respectively. We need to compare $r$ and $r'$. What could be the researched value of $r$ and $r'$?
A) 1, 1
B) 2, 2
C) 0, 1
D) 1, 0
E) 0, 0

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