
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 paper rectangle \(3 \times 100\) divided into 300 \(1 \times 1\) cells. What is the maximum number of pairs consisting of one "corner" and one \(2 \times 2\) square that can be cut out along the grid lines? (A "corner" is created from a \(2 \times 2\) square by removing one of its corner cells).

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