
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 $f(x)=\ln x$, $g(x)= \frac {a}{x}$, let $F(x)=f(x)+g(x)$.  
(Ⅰ) When $a=1$, find the monotonic interval of the function $F(x)$.  
(Ⅱ) If the slope $k$ of the tangent line at any point $P(x_0, y_0)$ on the graph of the function $y=F(x)$ $(0<x\leq 3)$ always satisfies $k\leq \frac {1}{2}$, find the minimum value of the real number $a$.

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