
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
Given a loan amount \(c\) that decreases each year and the new balance \(V\) after \(n\) years is calculated as \(V = \frac{c}{(1 + t)^{3n}}\), where \(t\) is the annual reduction rate, calculate the value of \(n\) if the original amount \(c\) and current balance \(V\) are known.

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