
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 $f\left( x \right)=x^{3}-6x^{2}+ax+b\left( a,b\in R \right)$ whose graph intersects the $x$-axis at a point where the tangent line is $y=9x-18$.

(1) Find the analytical expression of $f\left( x \right)$;

(2) If $21x+k-80 < f\left( x \right) < 9x+k$ holds true for $x\in \left( 1,5 \right)$, find the range of values for $k$.

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