
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
Given a set $U=\{a, b, c, d\}$, select 4 different subsets that must satisfy the following two conditions: (1) Both $\emptyset$ and $U$ must be selected; (2) For any two selected subsets $A$ and $B$, either $A \subseteq B$ or $B \subseteq A$ must hold. How many different ways are there to make such a selection?

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