
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
Given real numbers $x$, $y$, real numbers $a>1$, $b>1$, and $a^x = b^y = 2$,
(1) If $ab=4$, then the value of $\frac{1}{x} + \frac{1}{y}$ is __________;
(2) If $a^2+b=8$, then the maximum value of $\frac{2}{x} + \frac{1}{y}$ is __________.

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