
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
Let $\triangle ABC$ have internal angles $A$, $B$, $C$ opposite to sides $a$, $b$, $c$ respectively, and $\cos B=\frac{4}{5}, b=2$,

$(1)$ If $A=30^{\circ}$, find $a$

$(2)$ If the area of $\triangle ABC$ is $3$, find $a+c$.

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