
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
Let 
\[ 
g(n) = \dfrac{7+4\sqrt{7}}{14}\left(\dfrac{1+\sqrt{7}}{2}\right)^n + \dfrac{7-4\sqrt{7}}{14}\left(\dfrac{1-\sqrt{7}}{2}\right)^n. 
\]
Then compute $g(n+2) - g(n-2)$ and express it in terms of $g(n)$.
A) $2g(n)$  
   B) $g(n)$  
   C) $3g(n)$  
   D) $4g(n)$  
   E) $5g(n)$

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