
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 $f(x)=|\ln x|$, the solution set of the inequality $f(x)-f(x_{0})\geqslant c(x-x_{0})$ with respect to $x$ is $(0,+\infty)$, where $x_{0}\in(0,+\infty)$, and $c$ is a constant. When $x_{0}=1$, the range of $c$ is _______; when $x_{0}= \frac {1}{2}$, the value of $c$ is _______.

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