
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
Define a function $f(n) = \left\{ \begin{matrix} \log_{4}{n} & \text{if } \log_{4}{n} \text{ is rational} \\ 0 & \text{otherwise} \end{matrix}\right.$ for any positive integer $n$. Calculate $\sum_{n = 1}^{2000}{f(n)}$.
A) 10
B) 12
C) 15
D) 20
E) 30

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