
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 $2014=\alpha_k \cdot 5^k + \alpha_{k-1} \cdot 5^{k-1} + \ldots + \alpha_1 \cdot 5^1 + \alpha_0 \cdot 5^0$, where $\alpha_k, \alpha_{k-1}, \ldots, \alpha_0 \in \mathbb{N}$, $0 < \alpha_k < 5$, and $0 \leq \alpha_{k-1}, \alpha_{k-2}, \ldots, \alpha_1, \alpha_0 < 5$, determine the probability that a point P with x-coordinate and y-coordinate randomly selected from $\alpha_0, \alpha_1, \ldots, \alpha_k$ satisfies the equation $\frac{x^2}{16} + \frac{y^2}{9} = 1$.

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