
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
A 9x9 chessboard has its squares labeled according to the formula \(\frac{1}{r+c-2}\) where \(r\) is the row number and \(c\) is the column number, both ranging from 1 to 9. Nine squares are to be chosen such that exactly one square is chosen in each row and each column. Find the minimum sum of the labels of the nine chosen squares.

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