
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  $8 \times 8$  board is given, with sides directed north-south and east-west.
It is divided into  $1 \times 1$  cells in the usual manner. In each cell, there is most one *house*. A house occupies only one cell.

A house is *in the shade* if there is a house in each of the cells in the south, east and west sides of its cell. In particular, no house placed on the south, east or west side of the board is in the shade.

Find the maximal number of houses that can be placed on the board such that no house is in the shade.

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