
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 $M = 36 \cdot 36 \cdot 75 \cdot 224$. Determine the ratio of the sum of the odd divisors of $M$ to the sum of the even divisors of $M$.

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