
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 $f(x)=2|x-a|-x+a$, where $a>0$.  
$(1)$ If the area enclosed by the curve $y=f(x)$ and the line $y=a$ is $\frac{8}{3}$, find the value of $a$.  
$(2)$ Find the solution set of the inequality $f(x)>x$.

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