
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
For an upcoming holiday, the weather forecast predicts a $30\%$ probability of rain on the first day and a $40\%$ probability on the second day. If it rains on the first day, the probability of rain on the second day increases to $70\%$. What is the probability that it rains on at least one of the two days, assuming the initial independence unless it rains on the first day?

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