
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
Extend a rectangular pattern of 12 black and 18 white square tiles by attaching a border of white tiles around the rectangle. The original rectangle is 5x6 tiles and the border adds one tile to each side. Calculate the ratio of black tiles to white tiles in the extended pattern.

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