
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
Elective 4-5: Special Topics on Inequalities

Given the function $f(x)=|2x-3|+|2x+2|$.

$(1)$ Solve the inequality $f(x) < x+5$;

$(2)$ For any $x \in \mathbb{R}$, if $f(x) > a+\frac{4}{a}$ holds, find the range of the real number $a$.

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