
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,-2) $ and $ \overrightarrow{b}=(1,\cos \theta) $ are perpendicular to each other, where $\theta \in \left(0, \frac{\pi}{2}\right)$.

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

$(2)$ If $\sin (\theta-\phi)= \frac{ \sqrt{10}}{10}, 0 < \phi < \frac{\pi}{2} $, find the value of $\cos \phi$.

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