
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
Suppose that  $7$  boys and  $13$  girls line up in a row. Let  $S$  be the number of places in the row where a boy and a girl are standing next to each other. Calculate the average value of  $S$  (if all possible orders of the 20 people are considered).

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