
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
Jack wants to ride his bike in a circular track consisting of ten stops, starting and finishing at stop 0. He must visit stop 8 after visiting stop 5 but before reaching stop 0 again. There are dangerous stops at stop 3 and stop 7 that Jack must avoid completely. Determine the number of valid sequences of stops that Jack can make.

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