
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 $f(x)=(x+2)|x-2|$.
$(1)$ If the inequality $f(x) \leqslant a$ holds true over the interval $[-3,1]$, find the range of values for the real number $a$;
$(2)$ Solve the inequality $f(x) > 3x$.

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