
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
Each football ticket costs 50 yuan, and the ticket office does not prepare change. There are `m` people each holding a 50 yuan bill, and `n` people each holding a 100 yuan bill (where `m ≥ n`). Everyone lines up to buy tickets, with each person limited to purchasing one ticket. If everyone can buy their ticket without waiting for change, it is called a successful purchase. Find the probability of a successful purchase.

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