
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 $V$ consisting of elements "rib" and "taa", and the following postulates: $Q_1$: Every rib is a collection of taas, $Q_2$: Any two distinct ribs have two and only two taas in common, $Q_3$: Every taa belongs to exactly three ribs, $Q_4$: There are exactly six ribs. Consider the theorems: $U_1$: There are exactly fifteen taas, $U_2$: There are exactly five taas in each rib, $U_3$: For each taa there is exactly one other taa not in the same rib with it. Identify the theorems that can be deduced from the postulates.
A) U_1 only
B) U_2 and U_3 only
C) U_1 and U_2 only
D) U_1 and U_3 only
E) All

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