
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 $T=\lbrace a, b, c, d, e, f\rbrace$ is given. Two subsets of $T$ need to be selected such that their union equals $T$ and their intersection contains exactly three elements. The order of subset selection is irrelevant. Determine the number of ways this can be achieved.
A) 135
B) 250
C) 270
D) 540
E) 1080

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