
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 $f(x)= \frac{1}{3}x^3-2x^2+\frac{8}{3}x+1$ and the general term formula of the sequence $\{a_n\}$ is $a_n=2n-7$, calculate the value of $f(a_1)+f(a_2)+\ldots+f(a_8)$.

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