
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 have two positive integers both less than  $1000$ . The arithmetic mean and the geometric mean of these numbers are consecutive odd integers. Find the maximum possible value of the difference of the two integers.

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