
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 $f(x)$ is an even function, and $f(x)$ is increasing on $(-\infty, 0)$, and $f(2a^2-3a+2) < f(a^2-5a+9)$. It is known that the set of $a$ that satisfies the condition is the solution set of the inequality $2a^2+(m-4)a+n-m+3>0$. Find the values of $m$ and $n$.

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