
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
Chubby designs another nonstandard checkerboard, but this time it has 33 squares on each side. The board still follows the pattern of having a black square in every corner and alternates red and black squares along every row and column. Determine how many black squares are there on this checkerboard.

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