
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 to angles $A$, $B$, $C$ are respectively $a$, $b$, $c$, and also given $a=2$, $\cos B= \frac {4}{5}$.

$(1)$ If $b=3$, find the value of $\sin A$;

$(2)$ If the area of $\triangle ABC$, denoted $S_{\triangle ABC}$, equals $3$, find the values of $b$, $c$.

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