
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
The parabolas \(y = ax^2 + 3\) and \(y = 5 - bx^2\) intersect the coordinate axes in four points, forming a kite with an area of 20. Calculate \(a+b\).
A) \(\frac{1}{100}\)
B) \(\frac{1}{50}\)
C) \(\frac{1}{25}\)
D) \(\frac{1}{10}\)

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