
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
1. Given that tan($$\frac {π}{4}$$+α)=2, find the value of sin2α+cos<sup>2</sup>α.
2. Points A(x<sub>1</sub>, y<sub>1</sub>) and B(x<sub>2</sub>, y<sub>2</sub>) lie on a unit circle centered at the origin O. The minor arc $$\overparen {AB}$$ corresponds to a central angle α. If sinα+cosα= $$\frac {7}{17}$$, find the value of x<sub>1</sub>x<sub>2</sub>+y<sub>1</sub>y<sub>2</sub>.

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