
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
Given two sequences $\{a_n\}$ and $\{b_n\}$ whose sums of the first $n$ terms are $S_n$ and $T_n$ respectively, it is known that $S_{100} = 41$ and $T_{100} = 49$. Denote $C_n = a_nT_n + b_nS_n - a_nb_n$ (where $n \in \mathbb{N}^*$), find the sum of the first 100 terms of the sequence $\{C_n\}$, that is, calculate $$\sum_{i=1}^{100}C_i$$.

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