
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 $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $\cos C= \frac {3}{10}$.
(1) If $\overrightarrow{CA}\cdot \overrightarrow{CB}= \frac {9}{2}$, find the area of $\triangle ABC$;
(2) Let vectors $\overrightarrow{x}=(2\sin B,- \sqrt {3})$ and $\overrightarrow{y}=(\cos 2B,1-2\sin ^{2} \frac {B}{2})$, and $\overrightarrow{x}$ is parallel to $\overrightarrow{y}$, find the value of angle $B$.

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