
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
We write the integers from 1 to 2014 on the board. At each step, we erase two of them and write in their place their difference. Consequently, the number of integers decreases by 1. Can the last remaining integer at the two thousand and thirteenth step be equal to 0? Can it be equal to 1?

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