
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
Given the set \( A=\left\{\left.\frac{a_{1}}{9}+\frac{a_{2}}{9^{2}}+\frac{a_{3}}{9^{3}}+\frac{a_{4}}{9^{4}} \right\rvert\, a_{i} \in\{0,1,2, \cdots, 8\}, i=1, 2, 3, 4\} \), arrange the numbers in \( A \) in descending order and find the 1997th number.

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