
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 $c$ correspondingly. It is known that $\cos C = \frac{3}{5}$.
1. If $\overrightarrow{CB} \cdot \overrightarrow{CA} = \frac{9}{2}$, find the area of $\triangle ABC$;
2. Let vector $\overrightarrow{x} = (2\sin \frac{B}{2}, \sqrt{3})$ and vector $\overrightarrow{y} = (\cos B, \cos \frac{B}{2})$, and $\overrightarrow{x}$ is parallel to $\overrightarrow{y}$. Find the value of $\sin(B - A)$.

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