
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 p: "The line $x+y-m=0$ intersects with the circle $(x-1)^2+y^2=1$"; q: "The roots of the equation $x^2-x+m-4=0$ have different signs". If $p \lor q$ is true, and $\lnot p$ is true, find the range of the real number $m$.

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