
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 wand to make an object's length increase by $\frac{1}{3}$, meaning that if the length of the object was originally $x,$ then it is now $x + \frac{1}{3} x.$ On the second day he increased the object's longer length by $\frac{1}{4}$; on the third day he increased the object's new length by $\frac{1}{5}$; and so on. On the $n^{\text{th}}$ day of performing this trick, Barry will make the object's length exactly 50 times its original length. What is the value of $n$?

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