
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
In the sequence $\{a\_n\}$, $a\_n > 0$, $a\_1= \frac {1}{2}$. If $a\_{n+1}$ is the geometric mean of $1$ and $\frac {2a\_na\_{n+1}+1}{4- a\_ n^2 }$, then the value of $a\_1+ \frac {a\_2}{2^2}+ \frac {a\_3}{3^2}+ \frac {a\_4}{4^2}+… \frac {a\_{99}}{99^2}$ is \_\_\_\_\_\_.

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