
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
A bus ticket number consists of six digits. It is called a "lucky ticket" if the sum of the first three digits equals the sum of the last three digits. How many consecutive tickets must be purchased to ensure that at least one of them is a "lucky ticket"?
(Leningrad Mathematical Olympiad, 1987)

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