
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 hospital has the following employees:

- Sara Dores da Costa: rheumatologist
- Iná Lemos: pulmonologist
- Ester Elisa: nurse
- Ema Thomas: traumatologist
- Ana Lisa: psychoanalyst
- Inácio Filho: obstetrician

a) In how many ways can the employees form a line?

b) In how many ways can the same employees sit at a round table? Remember that at a round table, if everyone moves to the seat to their left, the table looks the same!

c) And in how many ways can the employees form a committee consisting of a president, vice-president, and substitute?

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