
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 $a_1, a_2, a_3, \dots,$ is defined recursively by $a_1 = 2, a_2 = 2,$ and for $k \ge 3,$
\[a_k = \frac{2}{5} a_{k - 1} + \frac{1}{6} a_{k - 2}.\]Evaluate $a_1 + a_2 + a_3 + \dotsb.$

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