
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 version of their game, Bernardo and Silvia start with an integer from $0$ to $999$. Bernardo performs a doubling operation ($B(x) = 2x$) and Silvia, instead of adding 50, adds $70$ ($S(x) = x + 70$). They continue to exchange outputs until one partner outputs a number that exceeds $1200$. Determine the smallest initial number, $N$, such that the final number Bernardo computes does not exceed $1200$ but any further operation by Silvia would exceed this limit. What is the sum of the digits of this $N$?
A) 0
B) 1
C) 2
D) 3
E) 4

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