
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 $y=a\left(x-3\right)^{2}+c$ ($a$ and $c$ are constants, $a \lt 0$). When the independent variable $x$ takes the values $\sqrt{5}$, $0$, and $4$, the corresponding function values are $y_{1}$, $y_{2}$, and $y_{3}$, respectively. The relationship between $y_{1}$, $y_{2}$, and $y_{3}$ is ____ (connected by "$ \lt $").

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