
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: for any $n∈N^{*}$, $a_{n+1}=ka_{n}+2k-2$, where $k$ is a constant not equal to $0$ or $1$. If $a_{i}∈\{-272,-32,-2,8,88,888\}$, where $i=2$, $3$, $4$, $5$, then the sum of all possible values of $a_{1}$ is $\_\_\_\_\_\_\_$.

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