
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
1. When $a=2$, $b=-3$, calculate the values of the algebraic expressions $(a-b)^2$ and $a^2-2ab+b^2$ respectively.  
2. Based on the results above, what relationship can you conjecture between the values of these two algebraic expressions? (If you cannot guess the relationship based on the results above, you may try calculating with a few more sets of values for $a$ and $b$ to conjecture.)  
3. Based on your conjecture, please calculate the value of the algebraic expression $a^2-2ab+b^2$ in a simpler way when $a=2012$, $b=2013$.

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