
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
Let $r, p,$ and $g$ be the number of marbles that Ringo, Paul, and George have, respectively. When each person places their marbles into bags holding 6 marbles each, the remainders of $r, p,$ and $g$ when divided by 6 are 5, 2, and 3, respectively. How many marbles will be leftover when they combine all their marbles into as many bags as possible, with each bag holding 6 marbles?

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