
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 a string of length n+1 composed of the letters α, β, and γ, the string must start with α and adjacent letters must be different. For example, when n=1, possible strings are αβ or αγ; when n=2, possible strings are αβα, αβγ, αγα, αγβ. If the number of such strings of length n+1 that end with the letter α is denoted by a<sub>n</sub>, find the value of a<sub>1</sub>+a<sub>2</sub>+…+a<sub>2018</sub>.

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