
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 square board is divided by seven lines parallel to one side of the board and seven lines parallel to the other side, into 64 rectangular cells, which are painted in white and black in a checkerboard pattern. The distances between neighboring lines are not necessarily equal, so the cells can be of different sizes. It is known, however, that the ratio of the area of any white cell to the area of any black cell is no more than 2. Find the greatest possible ratio of the total area of the white cells to the total area of the black cells.

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