
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
In a country with 100 cities, 30 are in the mountainous region, and 70 are in the plains. Over three years, air routes were established between the cities. Each year, 50 new routes were inaugurated: all the cities were randomly divided into 50 pairs, and a route was opened between the cities in each pair. After three years, it was found that out of the 150 routes, exactly 21 connect pairs of mountainous cities. How many routes connect pairs of plains cities?

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