
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
Consider the following different board configurations:
1. A 2x3 board entirely covered with checkers.
2. A 4x4 board where adjacent corners (2x2 squares each) are omitted.
3. A 3x7 board fully covered with checkers.
4. A 7x3 board fully covered with checkers.
5. A 5x5 board with a single 1x1 square removed from the center.

Which of these shapes CANNOT be completely covered by non-overlapping dominoes without leaving any open spots?
A) 2x3 board
B) 4x4 board with corners removed
C) 3x7 board
D) 7x3 board
E) 5x5 board with the center removed

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