
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, Carla Witchcraft used her magic to increase an object's length by $\frac{2}{3}$, meaning if the original length was $x$, then it became $x + \frac{2}{3}x$. For each following day, she increased the object's latest length by $\frac{k+3}{k+2}$ where $k$ is the number of days since starting. On the $n^{\text{th}}$ day, Carla aims to make the object's length exactly 200 times its original length. Determine the value of $n$.

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