
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 set of cells on a grid plane is called rook-connected if you can reach every cell in the set starting from any cell of the set by moving horizontally or vertically along the grid lines (like a rook in chess). What is the minimum number of cells that must be removed from a \( 3 \times 4 \) rectangle of cells so that the remaining set of cells is not rook-connected?

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