
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 $\overrightarrow{a}=(\cos θ,\sin θ)$ and $\overrightarrow{b}=(2,-1)$.
(1) If $\overrightarrow{a} \perp \overrightarrow{b}$, find the value of $\frac{\sin θ-\cos θ}{\sin θ + \cos θ}$;
(2) If $|\overrightarrow{a}- \overrightarrow{b}|=2$ and $θ \in (0, \frac{π}{2})$, find the value of $\sin (θ+ \frac{π}{4})$.

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