
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
Five students sign up for four sports competitions, with each person limited to one event. How many different ways can they sign up? Furthermore, if they compete for the championship in these four events, how many possibilities are there for winning the championship?

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