
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
There are 2012 balls in a row in red, yellow, and blue colors. The distance between any two adjacent balls is 1 centimeter. In every group of 4 consecutive balls, there is 1 red ball, 1 yellow ball, and 2 blue balls. The distance between the 100th red ball from the left and the 100th yellow ball from the right is 1213 centimeters. Find the distance between the 100th blue ball from the left and the 100th blue ball from the right in centimeters.

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