
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
The natural number \( X \) does not have zeros in its decimal representation and satisfies the equation \( X \cdot \bar{X} = 1000 + P(X) \). Here, \(\bar{X}\) denotes the number formed by the digits of \( X \) in reverse order, and \( P(X) \) is the product of the digits of the number \( X \). Find all such numbers.

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