
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 \[\begin{aligned} \lfloor x \rfloor + \{y\} &= 3.2, \\ \{x\} + \lfloor y \rfloor &= 4.7. \end{aligned} \]Compute $|x - y|$.

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