
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
Answer the following two questions and justify your answers:
(1) What is the last digit of the sum \(1^{2012}+2^{2012}+3^{2012}+4^{2012}+5^{2012}\) ?
(2) What is the last digit of the sum \(1^{2012}+2^{2012}+3^{2012}+4^{2012}+\cdots+2011^{2012}+2012^{2012}\) ?

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