
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
We need to determine a single-digit, a two-digit, and a three-digit natural number based on the following criteria.

The two-digit number is even, while the other two are odd.

If we multiply the numbers together, the product ends with 68, and preceding this is the sum of the three numbers, which is a perfect square.

If the hundreds digit of the three-digit number is placed in front of the two-digit number, the new three-digit number and the remaining two-digit number are both perfect squares.

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