
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 curve $x^{2}+y^{2}-2ax+2(a-2)y+2=0$, where $a\in\mathbb{R}$, when $a=1$, the trajectory represented by the curve is \_\_\_\_\_\_. When $a\in\mathbb{R}$ and $a\neq 1$, the above curve system always passes through the fixed point \_\_\_\_\_\_.

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