
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
Let  $T$  be the set of all 2-digit numbers whose digits are in  $\{1,2,3,4,5,6\}$  and the tens digit is strictly smaller than the units digit. Suppose  $S$  is a subset of  $T$  such that it contains all six digits and no three numbers in  $S$  use all six digits. If the cardinality of  $S$  is  $n$ , find all possible values of  $n$ .

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