
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
In the decimal system, a $(n+1)$-digit number $A=\overline{a_{n} a_{n-1} \ldots a_{1} a_{0}}$ is called the reverse of $A*=\overline{a_{0} a_{1} \ldots a_{n}}$. (Thus, the reverse of 759 is 957, and the reverse of 980 is 89.)

Find the four-digit numbers that "reverse" when multiplied by 9, meaning $9A = A^*$.

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