
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 $\theta\in(0, \frac{\pi}{2})$.

(Ⅰ) Find the values of $\sin \theta$ and $\cos \theta$;  
(Ⅱ) 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}
user