
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 that angle $α$'s terminal side is in the second quadrant and intersects the unit circle at point $P\left(m, \frac{\sqrt{15}}{4}\right)$.

$(1)$ Find the value of the real number $m$;

$(2)$ Find the value of $\frac{\sin \left(α- \frac{π}{2}\right)}{\sin \left(π+α\right)-\sin \left( \frac{3π}{2}-α\right)+1}$.

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