
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
A class needs to select 5 students from 5 boys and 3 girls to be class representatives for 5 different subjects. Calculate the number of ways to arrange this under the following conditions:  
(1) The number of girls assigned must be less than the number of boys;  
(2) Boy A must be a class representative, but he cannot be the representative for mathematics;  
(3) Girl B must be the class representative for Chinese, and Boy A must be a class representative but also cannot be the representative for mathematics.

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