
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
There is a 10x10 grid, where each cell in the grid is labeled with numbers according to the formula: 
\[ a_{ij} = \frac{1}{i + j - 1} \]
where \(i\) is the row index and \(j\) is the column index, starting from 1. You need to select ten cells such that no two cells are in the same row or column. Calculate the minimum possible sum of the labels of the selected cells.

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