
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
Let \( N = 48 \cdot 48 \cdot 55 \cdot 125 \cdot 81 \). What is the ratio of the sum of the odd divisors of \( N \) to the sum of the even divisors of \( N \)?
**A)** \( \frac{1}{1020} \)
**B)** \( \frac{1}{765} \)
**C)** \( \frac{1}{510} \)
**D)** \( \frac{1}{255} \)
**E)** \( \frac{1}{128} \)

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