
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
In a newly built road in a city, there are 12 streetlights. To save electricity without affecting normal lighting, three of these lights can be turned off. However, the lights at both ends cannot be turned off, nor can two adjacent lights be turned off. How many ways are there to turn off the lights?

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