
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 $30\%$, the probability it will rain on Saturday is $50\%$, and the probability it will rain on Sunday is $40\%$. Assuming the probability that it rains on any day is independent of the other days except that if it rains on Saturday, the probability it will rain on Sunday increases to $70\%$. What is the probability it will rain on all three days, expressed as a percent?

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