
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
Let \( m,n \in \mathbb{R} \), if the line \( (m+1)x+(n+1)y-2=0 \) is tangent to the circle \( (x-1)^{2}+(y-1)^{2}=1 \), determine the range of \( m+n \).

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