
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
For a positive integer $n,$ let
\[ G_n = 1^2 + \frac{1}{2^2} + \frac{1}{3^2} + \dots + \frac{1}{n^2}. \]
Compute
\[ \sum_{n = 1}^\infty \frac{1}{(n + 1) G_n G_{n + 1}}. \]

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