
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
Each day, Barry Sotter uses his magic to increase the length of an object as follows: On the first day, he increases the length by $\frac{1}{2}$; on the second day by $\frac{1}{3}$; on the third day by $\frac{1}{4}$; and so on. On the $n^{\text{th}}$ day, he increases the day's starting length by $\frac{1}{n+1}$. Barry wants the object’s length on the $n^{\text{th}}$ day to be exactly 50 times its original length. What is the value of $n$?

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