
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

A square grid of 16 dots contains the corners of nine \( 1 \times 1 \) squares, four \( 2 \times 2 \) squares, and one \( 3 \times 3 \) square, for a total of 14 squares whose sides are parallel to the sides of the grid. What is the smallest possible number of dots you can remove so that, after removing those dots, each of the 14 squares is missing at least one corner? Justify your answer by showing both that the number of dots you claim is sufficient and by explaining why no smaller number of dots will work.

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