
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 $\{b_n\}$ are arithmetic sequences with a common difference of 1, and their first terms are $a_1$ and $b_1$ respectively, with $a_1 + b_1 = 5$, and $a_1, b_1 \in \mathbb{N}^*$. Let $c_n = a \cdot b_n$ ($n \in \mathbb{N}^*$), calculate the sum of the first 10 terms of the sequence $\{c_n\}$.

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