
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
Suppose we have a  $8\times8$  chessboard. Each edge have a number, corresponding to number of possibilities of dividing this chessboard into  $1\times2$  domino pieces, such that this edge is part of this division. Find out the last digit of the sum of all these numbers.

(Day 1, 3rd problem
author: Michal Rolínek)

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