
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 $B = (b_1, b_2, \dots, b_n)$ of numbers, the Cesaro sum of $B$ is defined as:
\[
\frac{T_1 + T_2 + \cdots + T_n}{n},
\]
where $T_k = b_1 + b_2 + \cdots + b_k$ and $1 \le k \le n$.

If the Cesaro sum of the 200-term sequence $(b_1,\dots,b_{200})$ is 300, what is the Cesaro sum of the 201-term sequence $(-1, b_1, \dots, b_{200})$?

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