
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
In triangle \(ABC\), the sides opposite angles \(A\), \(B\), and \(C\) are \(a\), \(b\), and \(c\) respectively. Given that \(\sin A= \frac{3}{5}\), \(\tan (A-B)= \frac{1}{3}\), and angle \(C\) is obtuse, with \(b=5\).
\((1)\) Find the value of \(\sin B\);
\((2)\) Determine the length of side \(c\).

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