
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
On a chessboard, each square’s label is determined by the formula $\frac{1}{2r_i + j - 1}$, where $r_i$ represents the row number of the chosen square in column $j$. Eight squares are chosen such that there is exactly one chosen square in each row and each column. Find the maximum sum of the labels of the eight chosen squares.

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