
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
In a \((2b+1) \times (2b+1)\) checkerboard, two squares not lying in the same row are randomly chosen. If \(c\) is the number of combinations of different pairs of squares chosen, find the value of \(c\).

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