
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
70 numbers are arranged in a row. Except for the first and last number, three times each number exactly equals the sum of its two adjacent numbers. The sequence starts with the following numbers on the far left: \(0, 1, 3, 8, 21, \cdots\). What is the remainder when the rightmost number is divided by 6?

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