
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
Let $[z]$ denote the greatest integer not exceeding $z$. Suppose $x$ and $y$ satisfy the simultaneous equations 
\begin{align*} 
y&=4[x]+1 \\ 
y&=2[x-1]+7. 
\end{align*}
If $x$ is not an integer, determine the value of $x+y$.
A) Between 10 and 11
B) Between 11 and 12
C) Between 12 and 13
D) Between 13 and 14

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