
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 a classroom activity where students have to cover different sized checkerboards using non-overlapping dominoes. Which of the following "checkerboards" CANNOT be covered exactly and completely by the dominos if a domino covers exactly two adjacent squares?
1. **5x3** checkerboard except for one missing square at the corner.
2. **4x4** checkerboard where all squares are present.
3. **5x5** checkerboard missing two squares diagonally adjacent from one corner to another.
4. **4x6** checkerboard fully intact.
5. **7x2** checkerboard without any squares missing.
A) 5x3 with one corner square missing.
B) 4x4 with all squares intact.
C) 5x5 missing two squares diagonally adjacent from one corner to another.
D) 4x6 fully intact.
E) 7x2 with all squares intact.

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