
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
Three subsets of the set $T=\lbrace p,q,r,s,t,u\rbrace$ are to be selected such that their union is $T$ and their intersection contains exactly three elements. How many ways can this task be accomplished, if the order in which the subsets are chosen matters?
A) 5000 
B) 6000 
C) 6860
D) 7000 
E) 8000

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