
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 real number pair \((x, y)\), where the maximum value of \(a = 2x^2 - y^2 + \frac{3}{2}\) and \(b = y^4 + 4x + 2\) does not exceed 1, determine the range of values for \((x, y)\) that meet this condition.



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