
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 "gib" and "naa", with the four postulates: $P_1$: Every gib is a collection of naas, $P_2$: Any two distinct gibs have two and only two naas in common, $P_3$: Every naa belongs to three and only three gibs, $P_4$: There are exactly five gibs. Determine if the three theorems are true: $T_1$: There are exactly ten naas, $T_2$: There are exactly four naas in each gib, $T_3$: Each naa pairs with exactly two other naas not in any common gib.
**A)** $T_1$ only  
**B)** $T_2$ only  
**C)** $T_1$ and $T_3$ only  
**D)** $T_2$ and $T_3$ only  
**E)** None

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