
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 the quadratic functions $y=-x^{2}+m^{2}x$ and $y=x^{2}-m^{2}$ (where $m$ is a constant), both graphs have two intersection points with the $x$-axis, and the distance between each pair of adjacent points among these four points is equal. Find the distance between the axes of symmetry of these two function graphs.

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