
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
In the Cartesian coordinate system $xoy$, with the $ox$ axis as the initial side, the terminal side of acute angle $\alpha$ intersects the unit circle in the first quadrant at point $A$, and the ordinate of point $A$ is $\frac{\sqrt{10}}{10}$. The terminal side of acute angle $\beta$ coincides with the ray $x-7y=0$ ($x\geq0$).  
(1) Find the values of $\tan\alpha$ and $\tan\beta$;  
(2) Find the value of $2\alpha+\beta$.

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