
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

In a $101 \times 101$ square, a corner square measuring $88 \times 88$ is painted red. What is the maximum number of non-attacking queens that can be placed on the board without placing any pieces on the red cells? A queen attacks in a straight line horizontally, vertically, and diagonally. It can attack through painted cells.

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