
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 $P$ be the least common multiple of all the integers $15$ through $35$, inclusive. Let $Q$ be the least common multiple of $P, 36, 37, 38, 39, 40, 41, 42, 43,$ and $45$. What is the value of $\frac{Q}{P}$?
A) 37
B) 1517
C) 65231
D) 2886
E) 74

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