
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
The probability it will rain on Friday is $40\%$, on Saturday it is $50\%$, and on Sunday it is $30\%$. If the probability it will rain on any given day is independent of the weather on any other day, except that if it rains on both Friday and Saturday, the probability of rain on Sunday increases to $60\%$. What is the probability it will rain on all three days?

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