
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
For $n$ a positive integer, define $Q(n)$ as the sum of the remainders when $n$ is divided by $3$, $5$, $7$, and $11$. For example, $Q(20) = 2 + 0 + 6 + 9 = 17$. How many three-digit positive integers $n$ satisfy $Q(n) = Q(n+1)$?
A) 7
B) 8
C) 9
D) 10
E) 11

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