
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
Consider the integers between $2000$ and $9999$, inclusive. What is the probability that a number chosen at random from this range is an even integer whose digits are all distinct and none of the digits is zero?
A) $\frac{21}{125}$
B) $\frac{1}{5}$
C) $\frac{28}{225}$
D) $\frac{7}{50}$
E) $\frac{9}{50}$

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