
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
Define
\[A = \frac{1}{2^2} + \frac{1}{4^2} - \frac{1}{8^2} - \frac{1}{10^2} + \frac{1}{14^2} + \frac{1}{16^2} - \dotsb,\] which omits all terms of the form $\frac{1}{n^2}$ where $n$ is an even multiple of 4, and
\[B = \frac{1}{4^2} - \frac{1}{12^2} + \frac{1}{20^2} - \frac{1}{28^2} + \frac{1}{36^2} - \frac{1}{44^2} + \dotsb,\] which includes only terms of the form $\frac{1}{n^2}$ where $n$ is an even multiple of 4.

Determine $\frac{A}{B}$.

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