
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
(1) Given $x > \frac{5}{4}$, find the minimum value of the function $y=4x+\frac{1}{4x-5}$.
(2) Given $a > 0, b > 0,$ and $2^a \cdot 4^b = 2$, find the minimum value of $\frac{2}{a} + \frac{1}{b}$.

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