
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
A sequence $b_1,$ $b_2,$ $b_3,$ $\dots,$ is defined recursively by $b_1 = 2,$ $b_2 = 3,$ and for $k \ge 3,$
\[b_k = \frac{1}{3} b_{k - 1} + \frac{1}{5} b_{k - 2}.\]Evaluate $b_1 + b_2 + b_3 + \dotsb.$

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