
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
By using the relationship between squaring and taking square roots as inverse operations, certain irrational numbers can be manipulated as follows: when $a=\sqrt{3}+1$, moving terms gives $a-1=\sqrt{3}$, squaring both sides gives $(a-1)^{2}=(\sqrt{3})^{2}$, so $a^{2}-2a+1=3$, which simplifies to the integer coefficient equation $a^{2}-2a-2=0$. Following the same method, complete the following problem: when $a=\frac{\sqrt{5}-1}{2}$, <br/>① the resulting integer coefficient equation is ______; <br/>② calculate $a^{3}-2a+2015=\_\_\_\_\_\_$.

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