
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
On the first day, Barry Sotter used his magic to make an object's length increase by $\frac{1}{3}$, so if the original length was $x$, it became $x + \frac{1}{3} x$. On the second day, he increased the new length by $\frac{1}{4}$; on the third day by $\frac{1}{5}$; and so on. On the $n^{\text{th}}$ day, Barry made the object's length exactly 50 times its original length. Find the value of $n$.

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