
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 proposition p: For $\forall x \in \mathbb{R}$, $y=\log(mx^2-4mx+m+3)$ is meaningful.  
(1) If proposition p is true, find the range of real number $m$;  
(2) Write out the proposition $\neg p$, if $\neg p$ is true, find the range of real number $m$.

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