
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 that point $A(x_{1}, y_{1})$ lies on the line $y=3x+19$, and points $B(x_{2}, y_{2})$ and $C(x_{3}, y_{3})$ lie on the parabola $y=x^{2}+4x-1$, where $y_{1}=y_{2}=y_{3}$ and $x_{1} < x_{2} < x_{3}$, calculate the range of $x_{1}+x_{2}+x_{3}$.

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