
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  $x$ ,  $y$ , and  $z$  be real numbers such that  $x<y<z<6$ . Solve the system of inequalities:
\[\left\{\begin{array}{cc}
\dfrac{1}{y-x}+\dfrac{1}{z-y}\le 2 
\dfrac{1}{6-z}+2\le x 
\end{array}\right.\]

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