
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 the quadratic polynomial \( f(x) = x^2 + ax + b \), it is known that for any real number \( x \), there exists a real number \( y \) such that \( f(y) = f(x) + y \). Find the maximum possible value of \( a \).

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