
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 
\( g(n) =\left\{\begin{matrix}\log_{4}{n}, &\text{if }\log_{4}{n}\text{ is rational,}\\ 0, &\text{otherwise.}\end{matrix}\right. \)
What is \( \sum_{n = 1}^{1023}{g(n)} \)?
**A** \( \frac{40}{2} \)  
**B** \( \frac{42}{2} \)  
**C** \( \frac{45}{2} \)  
**D** \( \frac{48}{2} \)  
**E** \( \frac{50}{2} \)

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