
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}^*\), \\(a_{n+1} = ka_n + 3k - 3\\), where \\(k\\) is a constant not equal to \\(0\\) or \\(1\\). If \\(a_i \in \{-678, -78, -3, 22, 222, 2222\}\\) for \\(i = 2, 3, 4, 5\\), then the sum of all possible values of \\(a_1\\) that meet the condition is

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