
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
Source: 2018 Canadian Open Math Challenge Part B Problem 2
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Let ABCD be a square with side length 1. Points  $X$  and  $Y$  are on sides  $BC$  and  $CD$  respectively such that the areas of triangels  $ABX$ ,  $XCY$ , and  $YDA$  are equal. Find the ratio of the area of  $\triangle AXY$  to the area of  $\triangle XCY$ .
[center]![Image](https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvZi9lLzAzZjhhYzU0N2U0MGY2NGZlODM4MWI4Njg2MmEyMjhlY2M3ZjgzLnBuZw==&rn=YjIuUE5H)[/center]

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