
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
In a modified game, Bernardo and Silvia start with an integer between $0$ and $1999$ inclusive. Bernardo triples any number he receives, and Silvia adds $100$ to any number she receives. The game continues until one of them produces a number greater than or equal to $3000$. The winner is the last person to produce a number less than $3000$. Determine the smallest initial number \( N \) that results in a win for Bernardo. What is the sum of the digits of \( N \)?
A) 8
B) 9
C) 10
D) 11
E) 12

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