
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 $a$, $b$, $c$ respectively, and it is given that $\sin \frac {B}{2}= \frac { \sqrt {5}}{5}$, and $\overrightarrow{BA} \cdot \overrightarrow{BC}=6$.  
$(1)$ Find the area of $\triangle ABC$;  
$(2)$ If $c+a=8$, find the value of $b$.

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