
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 $\alpha$, $\beta \in \left(0,\dfrac{\pi }{2}\right)$, $\cos \alpha =\dfrac{4}{5}$, $\cos \left(\alpha +\beta \right)=\dfrac{3}{5}$.

(1) Find the value of $\sin \beta$.

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

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