
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
If a sequence of numbers \(a_{1}, a_{2}, \cdots\) satisfies, for any positive integer \(n\),
$$
a_{n}=\frac{n^{2}+n-2-\sqrt{2}}{n^{2}-2},
$$

then what is the value of \(a_{1} a_{2} \cdots a_{2016}\)?

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