
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 $n=10.$ The rules for this iteration of the game are:

$\bullet$ Carolyn always has the first turn.
$\bullet$ Carolyn and Paul alternate turns.
$\bullet$ On her turn, Carolyn must remove one number from the list either if this number has at least one positive divisor other than itself remaining in the list, or if the number is prime.
$\bullet$ On his turn, Paul must remove all positive divisors of the number Carolyn has just removed.
$\bullet$ If Carolyn cannot remove any more numbers, Paul removes the rest of the numbers.

Suppose Carolyn removes the integer $3$ (which is prime) 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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