
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: The solution set of the equation $4x^2-2ax+2a+5=0$ has at most two subsets, and proposition q: $1-m \leq x \leq 1+m$, $m>0$. If $\neg p$ is a necessary but not sufficient condition for $\neg q$, find the range of the real number $m$.

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