
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 hospital, there are 12 internal medicine doctors and 8 surgeons. Now, 5 doctors must be selected to join a disaster relief medical team. Then:
(1) If a certain internal medicine doctor must participate and a certain surgeon cannot participate, how many ways can the team be selected?
(2) If at least one internal medicine doctor and at least one surgeon must participate, how many different teams can be formed?

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