
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 that $f(x)= \frac {4}{4^{x}+2}$, $S\_n$ is the sum of the first $n$ terms of the sequence $\{a\_n\}$, and $\{a\_n\}$ satisfies $a\_1=0$, and when $n \geqslant 2$, $a\_n=f( \frac {1}{n})+f( \frac {2}{n})+f( \frac {3}{n})+…+f( \frac {n-1}{n})$, find the maximum value of $\frac {a_{n+1}}{2S\_n+a\_6}$.

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