
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 sheriff believes that if he catches a number of bandits on a given day that is a prime number, then he is lucky. On Monday and Tuesday, the sheriff was lucky. Starting from Wednesday, the number of bandits he caught was equal to the sum of the number caught the day before yesterday and twice the number caught the day before. What is the maximum number of consecutive days the sheriff could be lucky this week? Justify your answer.

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