
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 is a $2n \times 2n$ checkerboard. Petya has placed $(n+1)^{2}$ chips on it. The cat can swipe any single chip onto the floor with one swipe, or it can swipe two chips that are in adjacent squares or diagonally adjacent squares with one swipe. What is the minimum number of swipes the cat will need to certainly knock all the chips off the board?

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