
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 as $a$, $b$, and $c$ respectively, with $a > c$. It is given that the area $S$ of $\triangle ABC$ is $\frac{3}{2}$, $\cos B = \frac{4}{5}$, and $b = 3\sqrt{2}$.

(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}
user