
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 $\{a\_n\}$ that satisfies the following property $(P)$: If $a\_p = a\_q$ where $(p, q ∈ ℕ^*)$, then $a_{p+1} = a_{q+1}$. If the sequence $\{a\_n\}$ has property $(P)$, and it is given that $a\_1 = 1$, $a\_2 = 2$, $a\_3 = 3$, $a\_5 = 2$, and $a\_6 + a\_7 + a\_8 = 21$, find the value of $a_{2017}$.

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