
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
(1) If a teacher and 6 students are to line up in a row, with the condition that the teacher cannot stand at either end, how many different arrangements are possible?  
(2) From 6 boys and 5 girls, 4 people are to be selected to participate in a competition, with the condition that there must be at least one boy and one girl among them. How many different selections are possible?  
(3) Originally, there are 3 programs on a schedule. If the relative order of these 3 programs remains unchanged, and 2 new programs are added, how many different arrangements are possible?

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