
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
Find the number of ordered triples of sets  $(T_1, T_2, T_3)$  such that
1. each of  $T_1, T_2$ , and  $T_3$  is a subset of  $\{1, 2, 3, 4\}$ ,
2.  $T_1 \subseteq T_2 \cup T_3$ ,
3.  $T_2 \subseteq T_1 \cup T_3$ , and
4.  $T_3\subseteq T_1 \cup T_2$ .

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