
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
On a piece of paper, there are 10 points drawn, with 8 blue points and 2 red points. The two red points are connected to all the blue points, but not to each other. All the blue points are connected to each other. When two points are connected, this connection is made by a single segment. In how many different ways can one travel from one red point to the other, passing through each point at most once?

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