
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
Let the sequence $\{a_n\}$ be an arithmetic sequence with the first term $2$ and common difference $d=1$, and the sequence $\{b_n\}$ be a geometric sequence with the first term $1$ and common ratio $q=2$. Find the sum $a_{b_1} + a_{b_2} + \cdots + a_{b_{10}}$.

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