
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 is a car-sharing parking lot where all the parking spaces are arranged in a row and are currently unoccupied. Assume that the first three cars that arrive and park at the lot park randomly, and the probability that these three cars do not park adjacent to each other is equal to the probability that exactly two of them park adjacent to each other. Determine the number of parking spaces in the lot.

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