
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
Let the function $f(x)=|2x+1|-|x-2|$.
$(1)$ Find the solution set of the inequality $f(x) > 2$;
$(2)$ For all $x \in \mathbb{R}$, make $f(x) \geqslant t^{2}- \dfrac {11}{2}t$, find the range of the real number $t$.

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