
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 $sinθ=\frac{{\sqrt{5}}}{5}$, where $\theta$ is an angle in the second quadrant.  
$(1)$ Find the value of $\frac{{cos({\frac{{3π}}{2}+θ})+cos({-θ})}}{{sin({\frac{π}{2}-θ})-cos({π+θ})}}$;  
$(2)$ Find the value of $cos({2θ-\frac{π}{6}})$.

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