
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
Consider a set of positive integers that satisfy the following conditions:

$\bullet$ I. The sum of the squares of their digits equals $65$,

$\bullet$ II. Each digit is larger than the one on its left.

What is the product of the digits of the largest integer that adheres to both conditions?

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