
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 chessboard where each square (i, j) is labeled with the number \(\frac{1}{i+j-1+2}\) where \(i\) and \(j\) correspond to the row and column indices, respectively. You must select exactly one square from each row and each column, and every selected square must lie on or above the main diagonal of the board. Calculate the minimum sum of the labels on the selected squares.

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