
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
Consider a permutation \( (b_1, b_2, b_3, b_4, b_5, b_6) \) of \( (1, 2, 3, 4, 5, 6) \). Define the permutation to be "difference-focused" if \( b_1 + b_2 + b_3 - b_4 - b_5 - b_6 > 0 \). Calculate the number of difference-focused permutations.
A) 960
B) 990
C) 1020
D) 1080
E) 1120

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