
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 defined by $g(n) = \dfrac{2 + \sqrt{2}}{4}\left(1 + \sqrt{2}\right)^n + \dfrac{2 - \sqrt{2}}{4}\left(1 - \sqrt{2}\right)^n$, determine $g(n+1) - g(n-1)$ in terms of $g(n)$.

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