
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
Suppose $n=10$ and Carolyn and Paul follow the updated rules of their number removal game:
- Carolyn always goes first and on each turn, she must remove the smallest number from the list that has at least one positive divisor other than itself remaining.
- Paul on his turn removes all positive divisors of the number that Carolyn just removed.
- The game ends when Carolyn cannot remove a number, following which Paul removes all remaining numbers.

If Carolyn removes the integer $3$ on her first turn, determine the sum of the numbers that Carolyn removes.

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