
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 $N = 36 \cdot 72 \cdot 50 \cdot 81$. Determine the ratio of the sum of the odd divisors of $N$ to the sum of the even divisors of $N$.
A) $1 : 120$
B) $1 : 125$
C) $1 : 126$
D) $1 : 130$

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