
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
On a street, there are 10 lamps numbered 1, 2, 3, …, 10. Now, we want to turn off four of them, but we cannot turn off two or three adjacent lamps, nor can we turn off the two lamps at both ends. How many ways are there to turn off the lamps under these conditions?

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