
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
An infinite geometric series representing the annual depreciation of an asset starts with a first term of $24$ (representing the initial depreciation) and a second term of $6$. A different depreciation model for another asset starts with the same initial depreciation of $24$, a second term of $6+n$, and a total depreciation over the years that is three times that of the first model. Find the value of $n$.

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