
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 \( n \), define:
\( f(n) = \left\{ \begin{matrix} \log_{4}{n}, & \text{if } \log_{4}{n} \text{ is rational,} \\ 0, & \text{otherwise} \end{matrix} \right. \)
What is \(\sum_{n = 1}^{255}{f(n)}\)?
A) $14$
B) $15$
C) $15.5$
D) $16$

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