
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 \( M = 45 \cdot 45 \cdot 98 \cdot 340 \). Find the ratio of the sum of the even divisors of \( M \) to the sum of the odd divisors of \( M \).
**A)** \( 10 : 1 \)  
**B)** \( 12 : 1 \)  
**C)** \( 14 : 1 \)  
**D)** \( 15 : 1 \)  
**E)** \( 16 : 1 \)

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