
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
Insert two digits into the number 2019 to form a six-digit number that:

- starts with 2 and ends with 9,
- is composed of six different digits,
- is divisible by three,
- its first three digits are divisible by three,
- its first four digits are divisible by four,
- the sum of the inserted digits is odd.

Determine the difference between the largest and smallest six-digit numbers with the given properties.

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