
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
The squares of a 9x9 chessboard are labelled with numbers by the following rule: the square in row \( i \) and column \( j \) is labelled \( \frac{1}{i+9-j} \), where \( i, j \) are from 1 to 9. Nine squares are to be 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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