
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
Consider the  $2\times3$  rectangle below. We fill in the small squares with the numbers  $1,2,3,4,5,6$  (one per square). Define a *tasty* filling to be one such that each row is **not** in numerical order from left to right and each column is **not** in numerical order from top to bottom. If the probability that a randomly selected filling is tasty is  $\frac{m}{n}$  for relatively prime positive integers  $m$  and  $n$ , what is  $m+n$ ?

    \begin{tabular}{|c|c|c|c|}
    \hline
          &   &   \hline
          &   &   \hline
    \end{tabular}

*2016 CCA Math Bonanza Lightning #4.2*

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