
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 $M$ be the number of ordered pairs of nonempty sets $\mathcal{C}$ and $\mathcal{D}$ satisfying the following conditions:
- $\mathcal{C} \cup \mathcal{D} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\}$
- $\mathcal{C} \cap \mathcal{D} = \emptyset$
- The number of elements in $\mathcal{C}$ is not an element of $\mathcal{C}$
- The number of elements in $\mathcal{D}$ is not an element of $\mathcal{D}$.
Find $M$.

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