
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 \( ABCD \) be a square with side length 1. Points \( X \) and \( Y \) are on sides \( BC \) and \( CD \) respectively such that the areas of triangles \( ABX \), \( XCY \), and \( YDA \) are equal. Find the ratio of the area of \( \triangle AXY \) to the area of \( \triangle XCY \).

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