
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 $0 < \alpha < \frac{\pi}{2}, 0 < \beta < \frac{\pi}{2}, \cos{\alpha} = \frac{3}{5}, \cos{(\beta + \alpha)} = \frac{5}{13}$.

(I) Find the value of $\frac{\sin{2\alpha}}{\cos^{2}{\alpha} + \cos{2\alpha}}$.

(II) Find the value of $\sin{\beta}$.

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