
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) Using Mirtes' idea, find the minimum number of employees the sector would need to ensure that two people have the same zodiac sign.

b) What is the minimum number of employees the sector would need to ensure that at least four of them have their birthdays on the same day of the week this year?

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