
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 that $x$ and $y$ are four-digit natural numbers, and $y > x$, $y = a \cdot 10^n$ (where $a$ is a one-digit natural number). Also, the sum of the thousands and hundreds digits of $x$ is exactly equal to the difference between $y$ and $x$, which is $5a$. Find $x$ and $y$.

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