
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
Consider the following sequence: \(1,0,1,0,1,0,2,3,\cdots\), where the terms starting from the 7th are defined as the remainder modulo 10 of the sum of the previous 4 terms. Do there exist six consecutive terms in the sequence that are \(0,1,0,1,0,1\)?

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