
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 $(x, y)$ be a solution to the system of equations:
\[
\begin{aligned} 
\lfloor x \rfloor + \{y\} &= 3.7, \\ 
\{x\} + \lfloor y \rfloor &= 8.2. 
\end{aligned} 
\]
Compute $|x - y|$.

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