
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 $\tan(\alpha+\beta)= \frac{2}{5}$ and $\tan\left(\beta- \frac{\pi}{4}\right)= \frac{1}{4}$, find the value of $\frac{\cos\alpha+\sin\alpha}{\cos\alpha-\sin\alpha}$;  
(2) Given $\alpha$ and $\beta$ are acute angles, and $\cos(\alpha+\beta)= \frac{\sqrt{5}}{5}$, $\sin(\alpha-\beta)= \frac{\sqrt{10}}{10}$, find $2\beta$.

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