
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
Trapezoid \(ABCD\) is inscribed in the parabola \(y = x^2\) such that \(A = (a, a^2)\), \(B = (b, b^2)\), \(C = (-b, b^2)\), and \(D = (-a, a^2)\) for some positive reals \(a, b\) with \(a > b\). If \(AD + BC = AB + CD\), and \(AB = \frac{3}{4}\), what is \(a\)?

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