
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 creates another nonstandard checkerboard, now with $33$ squares on each side. The checkerboard adheres to the same pattern rules, having a black square in every corner and alternating red and black squares along every row and column. Determine the number of black squares on this checkerboard.
A) 543
B) 544
C) 545
D) 546
E) 547

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