
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 10x10 chessboard where each square at position $(i, j)$ is labelled with a number $\frac{1}{i+j-1}$, with $i$ and $j$ representing the row and column indices respectively, running from 1 to 10. Select ten squares from this chessboard such that no two squares lie in the same row or the same column. Find the minimum possible sum of the labels of the ten selected squares.

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