
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
Given the sequence $\{a_n\}$, $a_n > 0$, $a_1= \frac {1}{2}$. If $a_{n+1}$ is the geometric mean between $1$ and $\frac {2a_{n}a_{n+1}+1}{4-a_{n}^{2}}$, calculate the sum $\sum_{n=1}^{100} \frac{a_n}{n^2}$.

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