
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 \( C \) consisting of \( n \) elements, in how many ways can we choose two subsets \( A \) and \( B \) such that:

a) The sets \( A \) and \( B \) do not intersect;

b) The set \( A \) is contained in the set \( B \)?

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