
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 four days, Mary Mixer uses her special mixing spoon to increase a potion's volume by various fractions each day. On the first day, she increases the volume by $\frac{1}{2}$, on the second day by $\frac{1}{4}$, on the third day by $\frac{1}{6}$, and on the fourth day by $\frac{1}{8}$. If this pattern continues, on the $n^{\text{th}}$ day Mary will make the potion volume exactly 150 times its original volume. What is the value of $n$?

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