
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
Among 6 internists and 4 surgeons, there is one chief internist and one chief surgeon. Now, a 5-person medical team is to be formed to provide medical services in rural areas. How many ways are there to select the team under the following conditions?  
(1) The team includes 3 internists and 2 surgeons;  
(2) The team includes both internists and surgeons;  
(3) The team includes at least one chief;  
(4) The team includes both a chief and surgeons.

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