
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
Let $\mathcal{T}$ be the set $\{1, 2, 3, \ldots, 15\}$. Let $n$ be the number of sets of two non-empty disjoint subsets of $\mathcal{T}$. Find the remainder obtained when $n$ is divided by $1000$.

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