
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 three days of January, there is a $\frac{1}{2}$ chance that it will snow where Claire lives. On each of the next four days, there is a $\frac{1}{3}$ chance that it will snow. What is the probability that it snows at least once during the first week of January?

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