
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 a quadratic function $y=ax^{2}+bx+c$ (where $a$, $b$, and $c$ are constants and $a\neq 0$), and it satisfies $a^{2}+2ac+c^{2} \lt b^{2}$. If the value of $y$ is the same when $x=t+2$ and $x=-t+2$ (where $t$ is any real number), find:<br/>
$(1)$ The symmetry axis of the parabola $y=ax^{2}+bx+c$ is the line ______;<br/>
$(2)$ If $y=2$ when $x=-2$, then the range of $a$ is ______.

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