
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
Determine the number of sequences of sets \( S_{1}, S_{2}, \ldots, S_{999} \) such that
\[ 
S_{1} \subseteq S_{2} \subseteq \cdots \subseteq S_{999} \subseteq \{1, 2, \ldots, 999\} .
\]

Here \( A \subseteq B \) means that all elements of \( A \) are also elements of \( B \).

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