
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
Under the call for the development of the western region by the country, a certain western enterprise received a $4$ million yuan interest-free loan for equipment renewal. It is predicted that after the equipment renewal, the income of the enterprise in the first month is $200,000$. In the following $5$ months, the income of each month increases by $20\%$ compared to the previous month. Starting from the $7$th month, the income of each month increases by $20,000$ more than the previous month. Then, starting from the use of the new equipment, the enterprise needs ______ months to repay the $4$ million interest-free loan with the income obtained. (Round the result to the nearest whole number)

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