
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 denoted by $a$, $b$, and $c$, respectively. It is given that $\sin A > \sin C$, $\vec{AB} \cdot \vec{BC} = -2$, $\cos B = \frac{1}{3}$, and $b = 3$.  
(1) Find the values of $a$ and $c$.  
(2) Find the value of $\cos(B - C)$.

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