
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 paging station has 3000 customers. If the station prepares 100 small gifts and invites customers to collect them at a specified time, assuming the probability of any one customer coming to collect a prize is 4%, can the paging station send an invitation for a gift to every customer? If it is to ensure that every prize collector receives a gift, how many gifts should the paging station prepare at least?

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