
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 market vendor has a basket of eggs. The first customer buys half of the eggs plus one more. The second customer buys half of the remaining eggs plus one more. The third customer also gets exactly half of the remaining eggs plus one more. How many eggs were there in the basket originally?

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