
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
Observe the following set of equations about non-zero real numbers $a$ and $b$:
$a^{2}-b^{2}=(a-b)(a+b)$
$a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$
$a^{4}-b^{4}=(a-b)(a^{3}+a^{2}b+ab^{2}+b^{3})$
...
By inductive reasoning, we can obtain the equation $a^{2015}-b^{2015}=(a-b)(x_{1}+x_{2}+x_{3}+…+x_{2015})$, where $x_{1}$, $x_{2}$, $x_{3}$, ..., $x_{2015}$ form a finite sequence ${x_{n}}$, then the general term formula for this sequence is $x_{n}=$ _______ ($1\leqslant n\leqslant 2015$, and $n\in N^{*}$) (The result is expressed using $a$, $b$, $n$)

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