
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]


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

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