
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 company specializes in making "boards with a hole": this is a $300 \times 300$ checkered board with a hole cut out in the shape of a rectangle, which does not extend to the edge of the board. Each such board is labeled with the maximum number of non-attacking rooks that can be placed on this board. (It is assumed that the rooks do not attack through the hole.) For the firm's anniversary, it was decided to create a board with the highest possible number on the label. What is this number?

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