
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
Find the locus of points $X$ such that $p A X^{2} + q B X^{2} + r C X^{2} = d$, where $A$, $B$, and $C$ are given points, and $p$, $q$, $r$, and $d$ are given numbers with the condition $p + q + r = 0$.

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