
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, there are 4 southern cities and 5 northern cities. Transportation connects each southern city with each northern city in both directions; there is no transportation between other pairs of cities. A traveler starts from a specific southern city and plans to visit all the southern cities once and return to the starting point. How many different routes for such a trip exist?

a) \(4! \times 5!\);

b) \(3! \times 5^4\);

c) \(4^4 \times 4!\);

d) \(3^4 \times 5!\);

e) another answer.

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