
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 function $f(n)=2+{{2}^{4}}+{{2}^{7}}+{{2}^{10}}+\\cdots +{{2}^{3n+10}}(n\\in N)$, determine the value of $f(n)$.

A) $\dfrac{2}{7}({{8}^{n}}-1)$
B) $\dfrac{2}{7}({{8}^{n+1}}-1)$
C) $\dfrac{2}{7}({{8}^{n+3}}-1)$
D) $\dfrac{2}{7}({{8}^{n+4}}-1)$

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