
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 1, and $\{b_n\}$ be a geometric sequence with the first term 1 and common ratio 2. Evaluate the sum $b_{a_{1}}+b_{a_{2}}+…+b_{a_{6}}$.

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