
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
(1) Given proposition p: $2x^2-3x+1\leq0$ and proposition q: $x^2-(2a+1)x+a(a+1)\leq0$, if $\neg p$ is a necessary but not sufficient condition for $\neg q$, find the range of the real number $a$.  
(2) Given proposition s: One root of the equation $x^2+(m-3)x+m=0$ is in the interval $(0,1)$, and the other root is in the interval $(2,3)$. Proposition t: The domain of the function $f(x)=\ln(mx^2-2x+1)$ is all real numbers. If $s \vee t$ is true, find the range of the real number $m$.

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