
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 are positive integers that have these properties:

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

$\bullet$ II. Each digit is no smaller than the one on its left.

What is the product of the digits of the largest integer with both properties?

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