
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
Find positive integers which comply with the following conditions:
1. The sum of the squares of their digits equals $82$.
2. Each digit in the number is larger than any digit to its left.
What is the product of the digits of the largest integer meeting these conditions?

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