
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 $α \in \left(0, \frac{\pi}{2}\right)$, and $f(a) = \cos α \cdot \sqrt{\frac{1-\sin α}{1+\sin α}} + \sin α \cdot \sqrt{\frac{1-\cos α}{1+\cos α}}$.  
$(1)$ Simplify $f(a)$;  
$(2)$ If $f(a) = \frac{3}{5}$, find the value of $\frac{\sin α}{1+\cos α} + \frac{\cos α}{1+\sin α}$.

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