
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 < α < \dfrac{π}{2} $, $0 < β < \dfrac{π}{2} $, $\cos α= \dfrac{3}{5}$, and $\cos \left(β+α\right)= \dfrac{5}{13}$.

(I) Find the value of $\sin β$;

(II) Find the value of $\dfrac{\sin 2α}{{\cos }^{2}α+\cos 2α}$.

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