
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 $y=(m-1)x^{2}+2mx+3$ is an even function, determine the relationship among $f(-1)$, $f(-\sqrt{2})$, and $f(\sqrt{3})$.

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