
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
Define: For a real number $x$, $\lfloor x \rfloor$ represents the greatest integer less than or equal to $x$, called the integer part of $x$, and $\{x\} = x - \lfloor x \rfloor$ is called the fractional part of $x$. Solve the equation: $\lfloor x \rfloor - 3\{x\} = 2$.

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