
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 the product of the digits of the largest integer such that:
$\bullet$ I. The sum of the squares of its digits is $41$.
$\bullet$ II. Each digit is larger than the one on its left.
$\bullet$ III. All digits are even numbers.

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