
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
(8 points) A hospital has 12 internal medicine doctors and 8 surgeons. Now, 5 doctors are needed to join the disaster relief medical team. Then:

(1) If a certain internal medicine doctor must participate, and a certain surgeon cannot participate, how many ways are there to choose?

(2) How many ways are there to choose if at least one internal medicine doctor and at least one surgeon must participate?

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