
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
Calculate the number of ways to arrange or select students under different conditions from a group of 7 students. Provide necessary calculation formulas and give the final answers numerically for the following scenarios:

(1) The number of ways to arrange the 7 students in a line such that student Bing does not stand in the middle.
(2) The number of ways to arrange the 7 students in a line such that students A, B, and C are not next to each other.
(3) The number of ways to arrange the 7 students in a line such that student A cannot stand at the very front or the very end (for science students).
(4) The number of ways to select 3 representatives from the 7 students for a speech, with the condition that at most two out of students A, B, and C are selected (for science students).
How many ways are there to select 3 representatives from the 7 students for a speech, with the condition that only one of students A and B is selected (for arts students)?

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