
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
In the 6th century BC, the Pythagorean school of ancient Greece discovered through the study of the construction of regular pentagons and regular decagons that the golden ratio is approximately $0.618$. This value can also be represented as $m=2\sin 18^{\circ}$. If $m^{2}+n=4$, then $\frac{m+\sqrt{n}}{\sin 63°}=\_\_\_\_\_\_$.

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