
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
Carolyn and Paul are playing a game starting with a list of integers from $1$ to $n$. In this variation:
- Paul always has the first turn.
- Carolyn and Paul alternate turns.
- On each of his turns, Paul must remove one number from the list such that this number has at least one positive divisor (other than itself) remaining in the list.
- On each of her turns, Carolyn must remove all positive divisors of the number that Paul has just removed.
- If Paul cannot remove any more numbers, then Carolyn removes the rest of the numbers.

Suppose $n=5$ and Paul removes the integer $3$ on his first turn. Determine the sum of the numbers that Carolyn removes.

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