
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 $\frac{1}{1}$, meaning that if the length of the object was originally $x$, then it is now $x + x$. On the second day, he increased the object's new length by $\frac{1}{2}$; on the third day, he increased it by $\frac{1}{3}$; and so on. On the $n^{\text{th}}$ day of performing this magic, Barry makes 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}
user