
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 $1$ to $n$, where $n=10$. Carolyn always starts and they alternate turns.

$\bullet$ Carolyn must remove one number from the list such that this number has at least two positive divisors other than itself remaining in the list.

$\bullet$ Paul must remove all of the positive divisors of the number that Carolyn has just removed.

$\bullet$ If Carolyn can't make a valid move, Paul removes the rest of the numbers.

Suppose 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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