
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
There was a meeting between Egyptians and Panamanians to discuss issues concerning the operation of the Suez and Panama Canals. There were a total of twelve participants at the meeting, with Egyptians outnumbering Panamanians. When the Egyptians arrived, they greeted each other in pairs in Arabic. Similarly, the Panamanians greeted each other in pairs in Spanish. However, the Panamanians and Egyptians did not exchange greetings with each other. Assuming there were a total of 31 exchanges of greetings, how many Egyptians and how many Panamanians were present at the meeting?

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