
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
In the city of Autolândia, car license plates are numbered with three-digit numbers ranging from 000 to 999. The mayor, Pietro, has decided to implement a car rotation system to reduce pollution, with specific rules for each day of the week regarding which cars can be driven:

- Monday: only cars with odd-numbered plates;
- Tuesday: only cars with plates where the sum of the three digits is greater than or equal to 11;
- Wednesday: only cars with plates that are multiples of 3;
- Thursday: only cars with plates where the sum of the three digits is less than or equal to 14;
- Friday: only cars with plates containing at least two identical digits;
- Saturday: only cars with plates strictly less than 500;
- Sunday: only cars with plates where all three digits are less than or equal to 5.

a) On which days can the car with plate 729 be driven?

b) Maria, the mayor's wife, wants a car that can be driven every day except Sunday. Which plate should she have?

c) Mayor Pietro needs a plate that allows him to drive every day. Which plate should he have?

d) Why can all inhabitants of Autolândia drive at least once a week?

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