
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 the plane vectors $\overrightarrow {a}=(4^{x}, 2^{x})$ and $\overrightarrow {b}=(1, \frac {2^{x}-2}{2^{x}})$, where $x\in\mathbb{R}$, if $\overrightarrow {a} \perp \overrightarrow {b}$, then $|\overrightarrow {a}- \overrightarrow {b}|= \_\_\_\_\_\_$.

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