
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 \( n \), if \( f(n) \) is defined as:
\[ f(n) = \begin{cases} 
\log_8 n & \text{if } \log_8 n \text{ is a rational number;} \\ 
0 & \text{if } \log_8 n \text{ is not a rational number.}
\end{cases} \]
Evaluate the sum \( \sum_{n=1}^{197} f(n) \).

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