
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
The squares of a chessboard are numbered from left to right and top to bottom (so that the first row reads \(1,2, \ldots, 8\), the second reads \(9,10, \ldots, 16\), and so forth). The number 1 is on a black square. How many black squares contain odd numbers?

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