
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
For a finite sequence \(B=(b_1,b_2,\dots,b_{150})\) of numbers, the Cesaro sum of \(B\) is defined to be
\[
\frac{T_1+\cdots+T_{150}}{150},
\]
where \(T_k = b_1 + \cdots + b_k\) for \(1 \leq k \leq 150\).

If the Cesaro sum of the 149-term sequence \((b_1,\dots,b_{149})\) is 200, what is the Cesaro sum of the 150-term sequence \((3, b_1, \dots, b_{149})\)?

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