
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 with integers from 1 to 10. The rules remain as before:
- Carolyn always starts, and they take turns.
- Carolyn can remove a number which has at least one positive divisor other than itself remaining.
- Paul removes all positive divisors of the number Carolyn removed in her turn.
- If Carolyn cannot act, then Paul removes the remaining numbers.

Suppose that $n=10$ and 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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