
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 $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, and $\sin A > \sin C$. Given that $\overrightarrow{AB} \cdot \overrightarrow{BC} = -2$, $\cos B = \frac{1}{3}$, and $b = 3$.

1. Find $a$ and $c$.
2. Find the value of $\cos (B - C)$.

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