
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

For any \( x \) and \( y \), the equality \( f(x + 2y) - f(x - 2y) = 4xy \) holds. It is also known that \( f(1) = 2 \). Find \( f(9) \).

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