
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  $N$  be the number of ways of choosing a subset of  $5$  distinct numbers from the set  $$ {10a+b:1\leq a\leq 5, 1\leq b\leq 5} $$  where  $a,b$  are integers, such that no two of the selected numbers have the same units digits and no two have the same tens digit. What is the remainder when  $N$  is divided by  $73$ ?

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