
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
Let \(I\) be the set of points \((x, y)\) in the Cartesian plane such that
\[ x > \left( \frac{y^4}{9} + 2015 \right)^{1/4} \]

Let \(f(r)\) denote the area of the intersection of \(I\) and the disk \(x^2 + y^2 \leq r^2\) of radius \(r > 0\) centered at the origin \((0,0)\). Determine the minimum possible real number \(L\) such that \(f(r) < L r^2\) for all \(r > 0\).

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