
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 given fractional equation, the Chinese characters represent the digits $1, 2, 3, 4, 5, 6, 7, 8,$ and $9$. Different characters represent different digits. Given that "北" represents $1$ and "京" represents $9$, determine all possible three-digit integers represented by "奥运会". Additionally, provide the reasoning behind your solution.
$$
\frac{\text { 北 }}{\text { 京 }}=\frac{\text { 奥运会 }}{\text { 心想事成 }}
$$

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