
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 two undefined elements "dots" and "lines," and the four postulates: $P_1$: Every line is a collection of dots, $P_2$: Any two distinct lines have one and only one dot in common, $P_3$: Every dot belongs to three and only three lines, $P_4$: There are exactly five lines. Consider the three theorems: $T_1$: There are exactly ten dots, $T_2$: There are exactly four dots in each line, $T_3$: For each dot, there are exactly two other dots not in the same line with it. The theorems which are deducible from the postulates are:
A) $T_1$ only
B) $T_2$ and $T_3$ only
C) $T_1$ and $T_2$ only
D) $T_1$ and $T_3$ only
E) all

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