
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
A set $T = \{a, b, c, d, e, f\}$ is given. Two subsets of $T$ are to be chosen such that their union is $T$ and their intersection contains exactly three elements. How many ways can this be done, assuming the subsets are chosen without regard to order?
A) 70
B) 80
C) 90
D) 100
E) 110

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