
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
(1) Let the line $\frac{x}{a} + \frac{y}{b} = 1$ (where $a > 0$, $b > 0$) pass through the point $(1,1)$. Determine the minimum value of $a+b$.
(2) It is given that the function $y= \sqrt{(m^{2}-3m+2)x^{2}+2(m-1)x+5}$ has the domain $\mathbb{R}$. Find the range of real numbers $m$.

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