
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 famous Italian mathematician Fibonacci, while studying the reproduction of rabbits, discovered the following sequence of numbers: \\(1\\), \\(1\\), \\(2\\), \\(3\\), \\(5\\), \\(8\\), \\(…\\). This sequence is characterized by the fact that the first two numbers are both \\(1\\), and starting from the third number, each number is equal to the sum of the previous two numbers. Such a sequence of numbers \\(\\{a\_{n}\\}\\) is called a "Fibonacci sequence". Find the value of \\((a\_{1}a\_{3}-a\_{2}^{2})+(a\_{2}a\_{4}-a\_{3}^{2})+(a\_{3}a\_{5}-a\_{4}^{2})+…+(a\_{2015}a\_{2017}-a\_{2016}^{2})\\).

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