
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
A parabola $\Pi_{1}$ with its branches facing upwards passes through the points $(10,0)$ and $(13,0)$. Another parabola $\Pi_{2}$, also with its branches facing upwards, passes through the point $(13,0)$. It is also known that the vertex of the parabola $\Pi_{1}$ bisects the segment connecting the origin and the vertex of the parabola $\Pi_{2}$. What is the x-coordinate of the other point where the parabola $\Pi_{2}$ intersects the $x$-axis?

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