
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 the sequence $\{a_{n}\}$ is an arithmetic sequence with a first term of $2$ and a common difference of $1$, and the sequence $\{b_{n}\}$ is a geometric sequence with a first term of $1$ and a common ratio of $2$, calculate the value of ${a}_{{b}_{1}}+{a}_{{b}_{2}}+{a}_{{b}_{3}}+{a}_{{b}_{4}}$.

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