
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
The length of a rectangle was increased by $12\%$, and the width was increased by $15\%$. a) By what percentage is the area of the new rectangle greater than the area of the original rectangle? b) Find the ratio of the length to the width of the original rectangle, given that the perimeter of the new rectangle is $13\%$ greater than the perimeter of the original.

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