
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 vectors $$\overrightarrow {a}=(4^{x}+1, 2^{x})$$, $$\overrightarrow {b}=(y-1, y-k)$$, and $$\overrightarrow {a} \perp \overrightarrow {b}.$$  
(1) Find the expression for the function $y=f(x)$.  
(2) If the minimum value of the function $f(x)$ is -3, find the value of the real number $k$.  
(3) If for any real numbers $x_1$, $x_2$, $x_3$, there always exists a triangle with side lengths $f(x_1)$, $f(x_2)$, and $f(x_3)$, find the range of values for the real number $k$.

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