
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
There are 2011 street lamps numbered \(1, 2, 3, \ldots, 2011\). For the sake of saving electricity, it is required to turn off 300 of these lamps. However, the conditions are that no two adjacent lamps can be turned off simultaneously, and the lamps at both ends cannot be turned off. How many ways are there to turn off the lamps under these conditions? (Express your answer in terms of binomial coefficients).

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