
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 $f(x) = |2x+2| - |x-2|$.
- $(1)$ Find the solution set of the inequality $f(x) > 2$;
- $(2)$ Given $x \in \mathbb{R}$, $f(x) < 2 - \frac{7}{2} t$ has a solution, find the range of the real number $t$.

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