
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
Let \( A=\{3+10k, 6+26k, 5+29k, k=1,2,3,4, \cdots\} \). Determine the smallest positive integer \( r \) such that there exists an integer \( b \) with the property that the set \( B=\{b+rk, k=1,2,3,4, \cdots\} \) is disjoint from \( A \).

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