
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 \( \left\{a_{n}\right\} \) defined by \( a_{1}=6 \) and \( a_{n+1}=\left[\frac{5}{4} a_{n}+\frac{3}{4} \sqrt{a_{n}^{2}-2}\right] \) for \( n \in \mathbb{Z}_{+} \), find the unit digit of \( S_{2016} \), where \( S_{n} \) is the sum of the first \( n \) terms of the sequence \( \left\{a_{n}\right\} \).

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