
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 points $A(-1, y_{1})$, $B(1, y_{2})$, $C(4, y_{3})$ all lie on the graph of the quadratic function $y=-(x-2)^{2}+m$, determine the relationship between $y_{1}$, $y_{2}$, and $y_{3}$.

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