
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
On a 9x9 checkerboard, the 81 whole numbers from 1 through 81 are written in order, starting with 1 in the top left corner and moving left to right, then top to bottom, and filling each row one by one. Calculate the sum of the numbers in the four corners of this 9x9 checkerboard.

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