
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
The one-variable quadratic equation about $x$ is $kx^{2}-6x+1=0$ and it has two real roots.<br/>$(1)$ Find the range of real number $k$;<br/>$(2)$ Let the two roots of the equation be $x_{1}$ and $x_{2}$, when $k$ is the largest integer that satisfies the condition, find the value of $x_{1}+x_{2}$.

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