
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
Parabola \(\Pi_{1}\) with upward-facing branches passes through points with coordinates \((10,0)\) and \((13,0)\). Parabola \(\Pi_{2}\) with upward-facing branches also passes through the point with coordinates \((13,0)\). It is also known that the vertex of parabola \(\Pi_{1}\) bisects the segment connecting the origin and the vertex of parabola \(\Pi_{2}\). At what x-coordinate does parabola \(\Pi_{2}\) intersect the \(x\)-axis again?

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