
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 sequence \(\left\{a_{n}\right\}\) is defined as follows:
\[ 
\begin{align*}
a_{1} &= 0, \\
a_{2} &= 1, \\
a_{n+1} &= \frac{\sqrt{6}-\sqrt{2}}{2} a_{n} - a_{n-1} \quad \text{for } n \geq 2.
\end{align*}
\]

Determine the value of \(a_{2019}\).

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