
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 \[f(n)=\dfrac{6+4\sqrt{3}}{12}\left(\dfrac{1+\sqrt{3}}{2}\right)^n+\dfrac{6-4\sqrt{3}}{12}\left(\dfrac{1-\sqrt{3}}{2}\right)^n.\] 
Compute $f(n+1) - f(n)$, expressed in terms of $f(n)$.
A) $\frac{\sqrt{3}-3}{4} f(n)$
B) $\frac{\sqrt{3}-3}{2} f(n)$
C) $\frac{\sqrt{3}}{4} f(n)$
D) $\frac{3-\sqrt{3}}{4} f(n)$

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