
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 integers from $10$ to $40$, inclusive. Let $Q$ be the least common multiple of $P$ and the integers $41, 42, 43, 44, 45, 46, 47, 48, 49,$ and $50$. What is the value of $\frac{Q}{P}?$
A) 1763
B) 82861
C) 9261
D) 14756

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