
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
For any positive integer $n$, let 
$$
f(n) =\left\{\begin{matrix}
\log_{10}{n}, & \text{if }\log_{10}{n}\text{ is rational,}\\ 
0, & \text{otherwise.}
\end{matrix}\right.
$$
What is $\sum_{n = 1}^{8000}{f(n)}$?
A) $0$
B) $3$
C) $6$
D) $10$

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