
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
Given vectors $\overrightarrow{a}=(\sin \theta ,1)$, $\overrightarrow{b}=(\cos \theta ,2)$ that satisfy $\overrightarrow{a}\parallel\overrightarrow{b}$, where $\theta\in(0, \frac{\pi}{2}) $.

(1) Find the values of $\sin \theta$ and $\cos \theta$;

(2) If $\cos (\theta+\phi)=- \frac{2 \sqrt{2}}{3}(0 < \phi < \frac{\pi}{2}) $, find the value of $\cos (\phi+ \frac{\pi}{2}) $.

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