
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
\[ A = \frac{1}{2^2} + \frac{1}{4^2} - \frac{1}{10^2} - \frac{1}{14^2} + \frac{1}{16^2} + \frac{1}{20^2} - \dotsb, \]
which omits all terms of the form $\frac{1}{n^2}$ where $n$ is an even multiple of 6, and
\[ B = \frac{1}{6^2} - \frac{1}{12^2} + \frac{1}{18^2} - \frac{1}{24^2} + \frac{1}{30^2} - \frac{1}{36^2} + \dotsb, \]
which includes only terms of the form $\frac{1}{n^2}$ where $n$ is an even multiple of 6.

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

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