
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
A rectangular grid of size 10x10 is labeled in such a way that each cell at the intersection of row \(i\) and column \(j\) is labelled as \(\frac{1}{2i+j}\). Ten cells are to be selected such that there is exactly one selected cell in each row and each column. Find the minimum sum of the labels of the ten selected cells.

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