
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
Let $f\left(x\right)$ be a function defined on $R$, and for any real number $x$, $f\left(1-x\right)=x^{2}-3x+3$.  
$(1)$ Find the analytical expression of the function $f\left(x\right)$;  
$(2)$ If the function $g\left(x\right)=|f\left(x\right)-ax+3|$ is monotonically increasing on $\left[1,3\right]$, find the range of real number $a$.

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