
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 $M$ be the least common multiple (LCM) of all the integers $15$ to $35$ inclusive. Let $N$ be the least common multiple of $M,36,37,38,39,40,41,42,43,44,$ and $45$. What is the value of $\frac{N}{M}$?
A) 132
B) 435
C) 9556
D) 65447
E) 123234

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