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

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

(2) Let $g\left( x \right)=f\left( x \right)-\dfrac{1}{2}{{x}^{2}}$. Find the range of the real number $a$ such that $g\left( x \right)\leqslant 0$ always holds when $x\in \left( 1,+\infty \right)$.

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