
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
On each of the first five days of January, there is a $\frac{1}{4}$ chance that it will snow where Jake lives. On the next five days, the probability alternates daily starting from $\frac{1}{3}$ on the 6th, $\frac{2}{5}$ on the 7th, $\frac{3}{7}$ on the 8th, $\frac{1}{2}$ on the 9th, and $\frac{1}{3}$ on the 10th. What is the probability that it snows at least once during the first ten days of January?

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