
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 $tan(α+β)= \frac{2}{5}$ and $tan\left(β- \frac{\pi}{4}\right)= \frac{1}{4}$, find the value of $$\frac{cosα+sinα}{cosα-sinα}$$.  
(2) Given that α and β are acute angles, and $cos(α+β)= \frac{\sqrt{5}}{5}$, $sin(α-β)= \frac{\sqrt{10}}{10}$, find the value of $2β$.  
(3) When solving problems involving known values of trigonometric functions to find the values of other trigonometric functions, what general approaches can be taken to find a solution? Please write out three methods.

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