
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
Bernardo and Silvia play a revised game where an integer between $0$ and $999$ inclusive is selected and given to Bernardo. Bernardo's move is to double the number, and Silvia's move is now to multiply the number by $3$. The game stops when a player's move results in a number greater than $999$, and the winner is the last person to produce a number less than $1000$. Let $M$ be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of $M$?
A) 7
B) 8
C) 9
D) 10
E) 11

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