
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
Jake is trying to remember John's phone number. He recalls that the first three digits are either 407, 410, or 413. For the last five digits, he knows they are made from the digits 0, 2, 4, 5, and 8, but he isn't sure about their order. If Jake dials a ten-digit number randomly adhering to these constraints, what is the probability that he dials John's correct number? Express your answer as a common fraction.

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