
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 $\frac{1}{2}$, meaning that if the length of the object was originally $l$, then it becomes $l + \frac{1}{2} l.$ On the second day, he increased the new length by $\frac{1}{3}$; on the third day, he increased it by $\frac{1}{4}$; and so on. On the $n^{\text{th}}$ day, Barry’s magic makes the object's length double its original length. Determine the value of $n$.

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