
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
Let $k,$ $p,$ and $q$ be real numbers, and let $A,$ $B,$ $C$ be points such that the midpoint of $\overline{BC}$ is $(k,0),$ the midpoint of $\overline{AC}$ is $(0,p),$ and the midpoint of $\overline{AB}$ is $(0,0).$ Find
\[\frac{AB^2 + AC^2 + BC^2}{k^2 + p^2}.\]

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