
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
The following table shows the air distances between five cities. If two different cities are chosen at random, what is the probability that the distance between them is less than $8000$ miles? Express your answer as a common fraction.

\begin{tabular}{|c|c|c|c|c|c|}
\hline
& Beijing & Cairo & Dublin & Manila & Rio de Janeiro \\ \hline
Beijing & & 4600 & 5000 & 1800 & 10300 \\ \hline
Cairo & 4600 & & 2400 & 8150 & 5600 \\ \hline
Dublin & 5000 & 2400 & & 6700 & 7900 \\ \hline
Manila & 1800 & 8150 & 6700 & & 11800 \\ \hline
Rio de Janeiro & 10300 & 5600 & 7900 & 11800 & \\ \hline
\end{tabular}

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