
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 areas of two squares are in the ratio \(16:49\). What is the ratio of their perimeters? Additionally, what is the ratio of the sum of their perimeters to the sum of their areas? Express your answers in simplest form.

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