
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 that the graph of a quadratic function intersects the $x$-axis at two points and the coordinates of the vertex are $\left(-2,1\right)$. If the graph passes through the points $(1,y_{1})$, $(-1,y_{2})$, $(-4,y_{3})$, then $y_{1}$, $y_{2}$, $y_{3}$ are connected by "$\lt$" as ______.

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