
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 $n\in\mathbb{N}^*$, we have $a_{n+1}=ka_n+2k-2$, where $k$ is a constant not equal to $0$ or $1$. If $a_i\in\{-272,-32,-2,8,88,888\},i=2,3,4,5$, then the sum of all possible values of $a_1$ that meet the conditions is.

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