
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 a function $f\left(x\right)$ defined on $R$ satisfies: $3f\left(2-x\right)-2f\left(x\right)=x^{2}-2x$.  
$(1)$ Find the analytical expression of the function $f\left(x\right)$;  
$(2)$ Given $a\in R$, solve the inequality $f\left(x\right)+a \gt 0$.

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