
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
There are six students who have signed up to participate in three intellectual projects, with a limit of one person per project and no limit on the number of projects each person can participate in. How many different ways can they sign up?

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