
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 the Land of Wonders, there are \( n \) cities connected by roads (any two cities are connected by at most one road). There are a total of \( a \) roads. It is assumed that if two cities are directly connected by a road, there is always an indirect path (i.e., a sequence of roads) to travel from one city to another. The Queen of Hearts has decreed that from now on, an even number of roads must extend from each city. Her minister proposes a list of all possible systems, totaling \( r \), obtained by removing some of the existing roads. What is the total number of roads appearing on this list (counting each road as many times as it appears)?

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