
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
Parabolas  $P_1, P_2$  share a focus at  $(20,22)$  and their directrices are the  $x$  and  $y$  axes respectively. They intersect at two points  $X,Y.$  Find  $XY^2.$ *Proposed by Evan Chang*

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