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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

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[ACTION NAME]

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# Your action step 2

# Your action step 3

...

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system
For a finite sequence \( B = (b_1, b_2, \dots, b_{199}) \) of numbers, the Cesaro sum of \( B \) is defined to be
\[ \frac{T_1 + \cdots + T_{199}}{199}, \]
where \( T_k = b_1 + \cdots + b_k \) and \( 1 \leq k \leq 199 \).

If the Cesaro sum of the 199-term sequence \( (b_1, \dots, b_{199}) \) is 2000, what is the Cesaro sum of the 200-term sequence \( (2, b_1, \dots, b_{199}) \)?

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