
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
A hospital has 12 internal medicine doctors and 8 surgeons. Five doctors are to be chosen to join the disaster relief medical team. The conditions are as follows:  
(1) Internal medicine doctor A and surgeon B must both join the team. How many different ways can the selection be made?  
(2) At least one of doctors A or B must join the team. How many different ways can the selection be made?

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