
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 \( m \), let 
\[ f(m) = \left\{ 
\begin{matrix}
\log_{9}{m}, & \text{if } \log_{9}{m} \text{ is rational} \\
0, & \text{otherwise}
\end{matrix} \right. \]
What is \( \sum_{m=1}^{1861} f(m) \)?
**A)** \(\frac{46}{3}\)
**B)** 10
**C)** 14
**D)** \(\frac{96}{3}\)
**E)** 20

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