
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
Given any two pairs of real numbers (a, b) and (c, d), it is defined that: (a, b) = (c, d) if and only if a = c and b = d. The operation "Ä" is defined as: (a, b) Ä (c, d) = (ac+bd, bc-ad); the operation "Å" is defined as: (a, b) Å (c, d) = (a + c, b + d). Let x and y be elements of R. If (3,4) Ä (x, y) = (11, -2), determine (3,4) Å (x, y).

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