
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 equation $mx^2-2x+1=0$ has real solutions". If "p ∨ q" is true and "¬q" is false, then find the range of the real number $m$.

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