
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 $f(x)=\left| \frac {3}{4}- \frac {1}{2}x\right|-\left| \frac {5}{4}+ \frac {1}{2}x\right|$,
(I) Find the range of the real number $a$ for which the inequality $f(x) \geq a^{2}-3a$ is always true with respect to $x$.
(II) If $f(m)+f(n)=4$ and $m < n$, determine the range of possible values for $m+n$.

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