
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
In a certain town, on each of the initial five days of January, the probability that it won't snow increases evenly from $\frac{1}{2}$ on the first day to $\frac{5}{6}$ on the fifth day. For each of the next two days, the probability of no snow is $\frac{7}{8}$. Calculate the probability that it snows at least once during these seven days.

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