
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 $f\left( x \right)=ax^{2}-\left( a+2 \right)x+ \ln x$.

(1) When $a=1$, find the equation of the tangent line to the curve $y=f\left( x \right)$ at the point $\left( 1,f\left( 1 \right) \right)$.

(2) If for any ${{x}_{1}},{{x}_{2}}\in \left( 0,+\infty \right),{{x}_{1}} < {{x}_{2}}$, it holds that $f\left( {{x}_{1}} \right)+2{{x}_{1}} < f\left( {{x}_{2}} \right)+2{{x}_{2}}$, find the range of values for $a$.

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