
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 the function $$f(x)=|x+ \frac {a}{x}|, (x>0)$, where $a$ is a real number.
1. When $a=-1$, determine the monotonicity of the function $y=f(x)$ on the interval $(1, +\infty)$ and provide a proof.
2. Discuss the minimum value of the function $y=f(x)$ based on different values of the real number $a$.

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