
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 of the board, creating 64 rectangular cells that are colored in a checkerboard pattern (alternating black and white). The distances between neighboring lines are not necessarily equal, so the cells may have different sizes. It is known that the ratio of the area of any white cell to the area of any black cell is at most 2. Find the maximum 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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