
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 $\lfloor x \rfloor$ denote the greatest integer less than or equal to $x$, $\lceil x \rceil$ denote the smallest integer greater than or equal to $x$, and $\langle x \rangle$ denote the integer closest to $x$ ($x \neq n + 0.5$, $n$ is an integer). Solve the equation $3\lfloor x \rfloor + 2\lceil x \rceil + \langle x \rangle = 8$ for $x$.

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