
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
A new road in a city is equipped with 12 streetlights. To save electricity without compromising on proper lighting, it is possible to turn off 3 of these lights. However, the lights at both ends of the road cannot be turned off, nor can two adjacent lights be turned off simultaneously. How many different methods are there to turn off 3 lights?

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