
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 $z$. Let $x$ and $y$ satisfy the simultaneous equations 
\begin{align*} 
y &= 4[x] + 2 \\
y &= 5[x - 3] + 7.
\end{align*}
If $x$ is not an integer, then find the value of $x+y$.
A) Between 50 and 51
B) Between 52 and 53
C) Between 54 and 55
D) Exactly 54

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