
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
Given six individuals: A, B, C, D, E, and F. (Please answer the following questions with numbers)
(1) If you invite these six individuals to participate in an event, where at least one person must attend but the exact number is up for you to decide, how many different scenarios are there for the invitation?
(2) Suppose all six individuals join six different events, each limited to one person. If individual A does not participate in the first event, and individual B does not join the third event, how many different arrangements are there?
(3) If these six individuals are assigned as facilitators to three different events, with at least one facilitator per event, what is the probability that D, E, and F are assigned to the same event?

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