
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
The Pythagorean school of ancient Greece studied the construction of regular pentagons and decagons in the 6th century BC and found that the value of the golden ratio is approximately $0.618$. This value can also be represented as $a=2\cos 72^{\circ}$. Then, $\frac{acos18°}{\sqrt{2-a}}=$____.

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