
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
Two subsets of the set $S=\lbrace a, b, c, d, e, f \rbrace$ are to be chosen so that their union is $S$ and their intersection contains exactly three elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter?
A) 20
B) 40
C) 60
D) 80
E) 160

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