
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
Given the sequence \(\left\{a_{n}\right\}\) satisfying \(a_{1}=a > 2\), \(a_{2017} = 2017\), and for any positive integer \(n\), \(a_{n+1} = a_{n}^{2} - 2\). Compute \(\left\lfloor \frac{\sqrt{a-2}}{10^{6}} a_{1} a_{2} \cdots a_{2017} \right\rfloor\), where \(\lfloor x \rfloor\) denotes the greatest integer not exceeding the real number \(x\).

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