
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
Say that a sequence  $a_1$ ,  $a_2$ ,  $a_3$ ,  $a_4$ ,  $a_5$ ,  $a_6$ ,  $a_7$ ,  $a_8$  is *cool* if
* the sequence contains each of the integers 1 through 8 exactly once, and
* every pair of consecutive terms in the sequence are relatively prime.  In other words,  $a_1$  and  $a_2$  are relatively prime,  $a_2$  and  $a_3$  are relatively prime,  $\ldots$ , and  $a_7$  and  $a_8$  are relatively prime.

How many cool sequences are there?

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