
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 that $a > b > 0$, $c < d < 0$, and $e < 0$, compare the magnitudes of $\frac{e}{a-c}$ and $\frac{e}{b-d}$.

(2) Given that $x > 0$, $y > 0$, and $2x+y=1$, find the range of $\frac{1}{x}+\frac{1}{y}$.

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