
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 $B=(b_1,b_2,\dots,b_{50})$ of numbers, the Cesaro sum of $B$ is defined to be
\[\frac{T_1+\cdots+T_{50}}{50},\]where $T_k=b_1+\cdots+b_k$ and $1\leq k\leq 50$.

If the Cesaro sum of the 50-term sequence $(b_1,\dots,b_{50})$ is 600, what is the Cesaro sum of the 51-term sequence $(2,b_1,\dots,b_{50})$?

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