
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 the equation $169x^2-bx+60=0$ has two roots, $\sin\theta$ and $\cos\theta$, where $\theta\in\left(\frac{\pi}{4}, \frac{3\pi}{4}\right)$.  
(1) Find the value of the real number $b$;  
(2) Calculate the value of $\frac{\sin\theta}{1-\cos\theta} + \frac{1+\cos\theta}{\sin\theta}$.

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