
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
The first four terms of an infinite sequence  $S$  of decimal digits are  $1$ ,  $9$ ,  $8$ ,  $2$ , and succeeding terms are given by the final digit in the sum of the four immediately preceding terms. Thus  $S$  begins  $1$ ,  $9$ ,  $8$ ,  $2$ ,  $0$ ,  $9$ ,  $9$ ,  $0$ ,  $8$ ,  $6$ ,  $3$ ,  $7$ ,  $4$ ,  $\cdots$ . Do the digits  $3$ ,  $0$ ,   $4$ ,   $4$  ever come up consecutively in  $S$ ?

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