
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
Given a road with 11 lampposts, determine the number of ways to turn off three of the lamps without turning off the lamps at both ends or two adjacent lamps at the same time.

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