
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
For the Olympic torch relay, it is planned to select 6 cities from 8 in a certain province to establish the relay route, satisfying the following conditions. How many methods are there for each condition?
(1) Only one of the two cities, A and B, is selected. How many methods are there? How many different routes are there?
(2) At least one of the two cities, A and B, is selected. How many methods are there? How many different routes are there?

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