
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. It is known that $a=5$ and $\sin A= \frac{\sqrt{5}}{5}$.
(1) If the area of triangle $ABC$ is $\sqrt{5}$, find the minimum value of the perimeter $l$.
(2) If $\cos B= \frac{3}{5}$, find the value of side $c$.

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