
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
Consider the sequence $a_1, a_2, \ldots, a_8$ that satisfies $a_1 = 2013$, $a_8 = 2014$, and $a_{n+1} - a_n \in \{-1, \frac{1}{3}, 1\}$ for $n=1, 2, \ldots, 7$. Find the total number of such sequences.

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