
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
We observed the lottery numbers listed in ascending order (Feb. 13, 1970, 25, 34, $49,68,75)$:

A) The fifth number is 3 times the first number.

B) The fourth number is twice the second number.

What is the probability of property $A$, the probability of property $B$, and the probability of both properties occurring simultaneously?

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