
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 $A(x\_1,y\_1)$ and $B(x\_2,y\_2)$ are any two points on the graph of the function $f(x)= \frac {1}{2}+ \log \_{2} \frac {x}{1-x}$, and $M$ is the midpoint of the segment $AB$ with an x-coordinate of $\frac {1}{2}$.

1. Find the y-coordinate of point $M$.
2. If $S\_{n}=f( \frac {1}{n})+f( \frac {2}{n})+…+f( \frac {n-1}{n})$, where $n∈N^{*}$ and $n≥slant 2$,
   1. Find $S\_{n}$;
   2. Given that $a\_{n}= \begin{cases} \frac {2}{3},n=1 \ \frac {1}{(S\_{n}+1)(S\_{n+1}+1)},n≥slant 2\end{cases}$, where $n∈N^{*}$, and $T\_{n}$ is the sum of the first $n$ terms of the sequence ${a\_{n}}$, find the smallest positive integer value of $λ$ such that $T\_{n}≤slant λ(S\_{n+1}+1)$ holds for all $n∈N^{*}$.

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