
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
$a$,$b$,$c$ are the opposite sides of angles $A$,$B$,$C$ in $\triangle ABC$. It is known that $\sqrt{5}a\sin B=b$.  
$(1)$ Find $\sin A$;  
$(2)$ If $A$ is an obtuse angle, and $b=\sqrt{5}$, $c=3$, find the perimeter of $\triangle ABC$.

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