
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
Written in each square of an infinite chessboard is the minimum number of moves needed for a knight to reach that square from a given square  $O$ . A square is called *singular* if  $100$  is written in it and  $101$  is written in all four squares sharing a side with it. How many singular squares are there?

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