
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 that $\sin\alpha = \frac{3}{5}$, and $\alpha \in \left(\frac{\pi}{2}, \pi \right)$. 
(1) Find the value of $\tan\left(\alpha+\frac{\pi}{4}\right)$; 
(2) If $\beta \in (0, \frac{\pi}{2})$, and $\cos(\alpha-\beta) = \frac{1}{3}$, find the value of $\cos\beta$.

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