
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 $a$, $b$, and $c$ correspond to angles $A$, $B$, and $C$ respectively, and satisfy $\sin\frac{B}{2}=\frac{\sqrt{5}}{5}$, $\overrightarrow{BA}\cdot\overrightarrow{BC}=6$.

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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