
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
An \(8 \times 8\) piece of land is divided into 64 \(1 \times 1\) squares. Rooms are to be built on this land such that each square can contain at most one room, and each room occupies exactly one square.

A room is considered shaded if there are rooms in the squares to its east, west, and south. Determine the maximum number of rooms that can be built on the land so that no room is shaded.

Note: A room located on the eastern, western, or southern boundary is not considered shaded by definition.

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