
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
Megan has lost Fatima's phone number again. This time, Megan remembers that the first two digits are either 27 or 30, and the last five digits are 2, 4, 5, 8, and 9, but she is sure that the number does not start or end with 5. If Megan dials a phone number at random that meets these conditions, what is the probability that she dials Fatima's correct number?

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