
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
Andover has a special weather forecast this week. On Monday, there is a  $\frac{1}{2}$  chance of rain. On Tuesday, there is a  $\frac{1}{3}$  chance of rain. This pattern continues all the way to Sunday, when there is a  $\frac{1}{8}$  chance of rain. The probability that it doesn't rain in Andover all week can be expressed as  $\frac{m}{n}$  for relatively prime positive integers  $m$  and  $n$ . Compute  $m+n$ .

*Proposed by Nathan Xiong*

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