
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
For any real number $x$, let $\lfloor x \rfloor$ denote the greatest integer less than or equal to $x$, and let $\{x\} = x - \lfloor x \rfloor$. If $x_1$, $x_2$, ..., $x_m (0 \leqslant x_1 < x_2 < … < x_m \leqslant 6)$ are all the real numbers in the interval $[0,6]$ that satisfy the equation $\lfloor x \rfloor \cdot \{x\} \cdot \lceil x \rceil = 1$, then the value of $x_1 + x_2 + … + x_m$ is $\boxed{\frac{95}{6}}$.

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