
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
Consider a 9x9 checkerboard where the whole numbers from 1 to 81 are written. The first 9 numbers are written in order across the first row, and this continues row by row. However, for this problem, the numbers in even rows are written in reverse order (i.e., the second row starts with 18 and ends with 10). Calculate the sum of the numbers in the four corners after all numbers are placed.
A) 160
B) 162
C) 164
D) 166
E) 168

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