
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 if the length of the object was originally $x$, then after the first day, it is $x + \frac{1}{3} x.$ On the second day, he increased the object's new length from the previous day by $\frac{1}{4}$; on the third day by $\frac{1}{5}$, and so on, with each day increasing the object's length by the next increment in the series $\frac{1}{n+3}$ for the $n^{\text{th}}$ day. If by the $n^{\text{th}}$ day Barry wants the object's length to be 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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