
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
There is a two-digit number \( x \) whose units digit and tens digit are different. If you swap the units and tens digits, you get another two-digit number \( y \). It is also given that \( x \cdot y \) equals a three-digit number \( z \), where the hundreds digit and the units digit of \( z \) are the same. Find \( x, y, z \).

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