
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
Ben the Bunny and Flash the Fox are ascending a staircase with a certain number of steps. Ben jumps up three steps at a time, while Flash jumps six steps at a time. If necessary, Ben will jump the last remaining step(s) if they are fewer than three, and Flash the last if fewer than six. It is known that Flash reaches the top with 11 fewer jumps than Ben. Calculate the sum of all possible numbers of steps this staircase can have and then find the sum of the digits of this sum.
A) 8
B) 9
C) 10
D) 11

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