
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 sequence $\{b_n\}$ with 8 terms satisfying $b_1=2014$, $b_8=2015$, and $b_{n+1}-b_n \in \{-1, \frac{1}{3}, 1\}$ (where $n=1,2,\ldots,7$), determine the total number of such sequences $\{b_n\}$.

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