
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 $y = ax^2 - 4$ and $y = 6 - bx^2$ intersect the coordinate axes in exactly four points, and these four points are the vertices of a kite of area $24$. Determine the value of $a + b$.

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