
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 10 different products produced by various factories:
(1) At a product selection event, 2 products are not eligible for selection. To choose 4 products and rank these 4 selected products, how many different selection methods are there?
(2) If 6 products are to be displayed in different positions, and the two products that won the gold medal must be included, how many different arrangement methods are there?

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