
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 parabola $y=x^{2}-\left(2m-1\right)x-6m$ intersects the $x$-axis at points $(x_{1}$,$0)$ and $(x_{2}$,$0)$, where $x_{1}x_{2}=x_{1}+x_{2}+49$. To make this parabola pass through the origin, it should be shifted to the right by ____ units.

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