
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 the squares are labeled as follows:
\[ \text{Label}(i, j) = \frac{1}{j + i + 2} \]
where \(i\) and \(j\) are the row and column indices, respectively, starting from 1. Nine squares are chosen such that there is exactly one chosen square 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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