
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
Mark thought of a three-digit number greater than 500 and said that if all odd digits in this number are replaced with \(A\) and all even digits with \(B\), the resulting pattern will be \(ABB\). If all digits divisible by three are replaced with \(V\) and all others with \(G\), the resulting pattern will be \(VVG\). List all three-digit numbers that meet these conditions.

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