
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 that the vertex of angle α coincides with the origin, the initial side coincides with the positive semi-axis of the x-axis, and the terminal side is on the line y=2x.
(1) Find the value of $cos(2α+ \frac {π}{4})$;
(2) Given that $α∈(0， \frac {π}{2})$, $sin(β+ \frac {π}{4})= \frac { \sqrt {10}}{10}$, $- \frac {π}{2}＜β＜0$, find the value of α-β.

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