
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
\[
y = 3[x] + 1
\]
\[
y = 4[x-1] + 2
\]
Given that $x$ is not an integer and $x$ is between 3 and 4, find the value of $x+y$.

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