
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
John believes that the first three digits of his friend Lucia’s phone are either 307, 308, or 312. The last four digits are 0, 2, 6, and 8, but he is unsure of their order. If John dials a number at random meeting these criteria, what is the probability that he correctly dials Lucia’s phone number? Express your answer as a common fraction.

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