
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 positive real numbers $x$, $y$, $z$ satisfy $x^{2}-3xy+4y^{2}-z=0$. Find the maximum value of $\frac{2}{x}+ \frac{1}{y}- \frac{2}{z}$ when $\frac{xy}{z}$ reaches its maximum.

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