
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
In a class of 28 students, 4 prizes are distributed. How many ways can this be done,

a) if the prizes are identical and each student can receive at most one prize?

b) if the prizes are identical and each student can receive more than one prize?

c) if the prizes are distinct and each student can receive at most one prize?

d) if the prizes are distinct and each student can receive more than one prize?

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