
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
Natural numbers \(a\), \(b\), and \(c\) greater than 2022 have the following properties:
- \(a + b\) is divisible by \(c - 2022\)
- \(a + c\) is divisible by \(b - 2022\)
- \(b + c\) is divisible by \(a - 2022\)

What is the greatest possible value of \(a + b + c\)?

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