
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 $f(x)=|x+3|+|x-a|$ $(a > 0)$.

$(1)$ When $a=4$, it is known that $f(x)=7$, find the range of $x$;

$(2)$ If the solution set of $f(x) \geqslant 6$ is $\{x|x\leqslant -4 \text{ or } x\geqslant 2\}$, find the value of $a$.

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