
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 that both sequences $\{a_{n}\}$ and $\{b_{n}\}$ are arithmetic sequences with a common difference of $1$, their first terms are $a_{1}$ and $b_{1}$ respectively, and $a_{1} + b_{1} = 5$, $a_{1} > b_{1}$, $a_{1}, b_{1} \in \mathbb{N}^* (n \in \mathbb{N}^*)$. Find the sum of the first 10 terms of the sequence $\{a_{b_{n}}\}$.

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