
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 $f(x)=-2x\ln x+x^{2}-2ax+a^{2}$. Let $g(x)$ be the derivative of $f(x)$.

(Ⅰ) If the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$ is perpendicular to the line $x+y+3=0$, find the value of $a$;  
(Ⅱ) Discuss the number of solutions to $g(x)=0$;

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