
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 $a=(\sin θ, -2)$ and $b=(1, \cos θ)$ are orthogonal to each other, where $θ∈(0,\dfrac{\pi }{2})$

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

(2) If $5\cos (θ -φ )=3\sqrt{5}\cos φ $, $0 < φ < \dfrac{\pi }{2}$, find the value of $\cos φ$

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