
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 $[x]$ as the greatest integer less than or equal to $x$, and $\{x\}=x-[x]$. Find all positive real numbers \( x, y, z \) that satisfy the following conditions:
\[
\left\{
\begin{array}{l}
\{x\} + [y] + \{z\} = 2.9, \\
\{y\} + [z] + \{x\} = 5.3, \\
\{z\} + [x] + \{y\} = 4.0.
\end{array}
\right.
\]

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