
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 the integers $1$ to $10$. The rules of the game are the same as described:
- Carolyn has the first turn.
- They alternate turns.
- Carolyn removes a number that has at least one positive divisor other than itself remaining in the list.
- Paul removes all of the positive divisors of the number that Carolyn has just removed.
- If Carolyn cannot remove any more numbers, then Paul removes the rest of the numbers.

Suppose that $n=10$ and Carolyn removes the integer $4$ 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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