
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 $\triangle ABC$ with sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ respectively, and $a=2$, $\cos B= \frac{3}{5}$.

$(1)$ If $b=4$, find the value of $\sin A$;

$(2)$ If the area of $\triangle ABC=S_{\triangle ABC}=4$, find the values of $b$ and $c$.

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