
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
Mr. Cheng bought a house for a total price of 800,000 yuan, with a down payment of 300,000 yuan. He applied for a loan of 500,000 yuan from the bank, with a monthly interest rate of 0.5%. He starts to repay the loan from the first month after obtaining the loan, with equal repayment amounts each month, and the loan is to be fully repaid in 30 years. How much should Mr. Cheng repay each month (accurate to 0.01 yuan)?

(Note: If Mr. Cheng owes the bank a loan of a yuan in the previous month, then one month later, Mr. Cheng should repay the bank a fixed amount of x yuan, at which point the loan balance will be a(1+0.5%)-x yuan)

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