
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
When a five-digit number, consisting of identical digits, is divided by a four-digit number, also made up of identical digits, the quotient is 16 and there is a certain remainder. After removing one digit from both the dividend and the divisor, the quotient remains unchanged, but the remainder decreases by 2000. Determine these numbers.

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