
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
Given a checkerboard with 31 rows and 29 columns, where each corner square is black and the squares alternate between red and black, determine the number of black squares on this checkerboard.

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