
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 a set \( S \) consisting of elements "pib" and "maa", defined by the following postulates: 
- \( P_1 \): Every pib is a set of maas.
- \( P_2 \): Any two distinct pibs have exactly two maas in common.
- \( P_3 \): Every maa belongs to exactly three pibs.
- \( P_4 \): There are exactly six pibs. 

Determine the total number of maas and how many maas each pib contains, considering the information provided.
A) 10 maas, 4 per pib
B) 10 maas, 5 per pib
C) 8 maas, 4 per pib
D) 12 maas, 6 per pib
E) 6 maas, 3 per pib

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