
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
Point A (1, 7) lies on the terminal side of an acute angle $\alpha$, and acute angle $\beta$ satisfies $\sin\beta= \frac{\sqrt{5}}{5}$.

(1) Find the value of $\tan(\alpha+\beta)$.

(2) Find the value of $\alpha+2\beta$.

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