
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
There are 8 products, among which there are 3 first-grade products, 3 second-grade products, and 2 third-grade products. Draw 4 products at random.  
(1) How many different ways are there to draw without any first-grade products?  
(2) How many different ways are there to draw with at least one product of each grade (first-grade, second-grade, and third-grade)?

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