
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 arithmetic sequence {a_n} and the geometric sequence {b_n} both have a first term of 1, and both have a common difference and common ratio of 2, respectively. Find the value of a_{b_2} + a_{b_3} + a_{b_4}.

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