
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 $f(x)=\ln x+ \frac {1}{2x}$.
- (I) Discuss the monotonicity of the function $f(x)$;
- (II) Let $g(x)=f(x)-m$. If the function $g(x)$ has exactly one zero in the interval $\left[ \frac {1}{e}, 1\right]$ (Note: $e$ is the base of the natural logarithm), find the range of the real number $m$.

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