
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
An independent set of a graph \( G \) is a set of vertices of \( G \) such that no two vertices among these are connected by an edge. If \( G \) has 2000 vertices, and each vertex has degree 10, find the maximum possible number of independent sets that \( G \) can have.

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