
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
In the plane rectangular coordinate system $xOy$, let proposition $p$: the line $l_{1}$: $x+my-1=0$ is parallel to the line $l_{2}$: $\left(m+2\right)x+3y-5=0$; proposition $q$: the circle $C:x^{2}+y^{2}-2mx-2my+2m^{2}-4=0\left(m\neq 0\right)$ intersects with the circle $O:x^{2}+y^{2}=4$. If proposition $p$ and proposition $q$ have exactly one true proposition, find the range of real number $m$.

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