
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 the initial investment P = 330,000 yuan, interest rate i = 10% = 0.10, and an annual withdrawal A = 82,500 yuan, determine the minimum number of years n required to recover all the principal and interest.

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