
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
Given an arbitrary floor plan composed of \( n \) unit squares, Albert and Berta want to cover this floor with tiles, each tile having the shape of a \( 1 \times 2 \) domino or a T-tetromino. Albert only has tiles of one color available, while Berta has dominoes of two colors and tetrominoes of four colors. Albert can cover this floor plan with tiles in \( a \) ways, and Berta in \( b \) ways. Assuming that \( a \neq 0 \), determine the ratio \( b / a \).

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