
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 certain country's football league, there are two levels: Division A and Division B. Division A has 12 teams, and Division B has 8 teams. It is required to select 5 teams to participate in an international invitational tournament.

  (1) If a specific Division A team, Team A, must participate, and a specific Division B team, Team B, cannot participate, how many ways are there to choose?

  (2) If at least one team from both Division A and Division B must participate, how many ways are there to choose?

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