
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
Suppose $2014=α_{k}⋅5^{k}+α_{k-1}⋅5^{k-1}+…+a_{1}⋅5^{1}+a_{0}⋅5^{0}$, where $a_{k}$, $a_{k-1}$, $…$, $a_{0}∈N$, $0 < a_{k} < 5$, $0≤slant a_{k-1}$, $a_{k-2}$, $…$, $a_{1}$, $a_{0} < 5$. Find the probability that a randomly selected point $P$, the coordinates of which are determined by any two distinct numbers from $a_{0}$, $a_{1}$, $…$, $a_{k}$, falls within the ellipse $\frac{x^{2}}{16}+ \frac{y^{2}}{9}=1$.

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