
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 $\overrightarrow {m}$=(sinα-2，-cosα), $\overrightarrow {n}$=(-sinα，cosα), where α∈R.
1. If $\overrightarrow {m}$⊥$\overrightarrow {n}$, find angle α;
2. If $|\overrightarrow {m}$-$\overrightarrow {n}$|=$\sqrt {2}$, find the value of cos2α.

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