
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 a segment of length $2$ with endpoints $A$ and $B$ sliding respectively on the $x$-axis and $y$-axis, the midpoint $M$ of segment $AB$ traces curve $C$.  
(Ⅰ) Find the equation of curve $C$;  
(Ⅱ) Point $P(x,y)$ is a moving point on curve $C$, find the range of values for $3x-4y$;  
(Ⅲ) Given a fixed point $Q(0, \frac {2}{3})$, investigate whether there exists a fixed point $T(0,t) (t\neq \frac {2}{3})$ and a constant $\lambda$ such that for any point $S$ on curve $C$, $|ST|=\lambda|SQ|$ holds? If it exists, find $t$ and $\lambda$; if not, explain why.

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