
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 points A$(x_1, y_1)$ and B$(x_2, y_2)$ are any two points (can be coincident) on the graph of the function $$f(x)= \begin{cases} \frac {2x}{1-2x}, & x\neq \frac {1}{2} \\ -1, & x= \frac {1}{2}\end{cases}$$, and point M is on the line $$x= \frac {1}{2}$$, with $$\overrightarrow {AM} = \overrightarrow {MB}$$.
(Ⅰ) Find the values of $x_1+x_2$ and $y_1+y_2$
(Ⅱ) Given $S_1=0$, for $n\geq2$, $S_n=f( \frac {1}{n})+f( \frac {2}{n})+f( \frac {3}{n})+\ldots+f( \frac {n-1}{n})$, find $S_n$;
(Ⅲ) Under the condition of (Ⅱ), let $a_n=2^{S_{n}}$, and $T_n$ be the sum of the first n terms of the sequence $\{a_n\}$. If there exist positive integers c and m such that the inequality $$\frac {T_{m}-c}{T_{m+1}-c} < \frac {1}{2}$$ holds, find the values of c and m.

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