
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 a square pattern of 9 black and 16 white square tiles, extend the pattern by attaching a border that consists of two alternating layers (black and white) around the square. What is 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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