
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 two days of January, there is a $\frac{1}{2}$ chance that it will snow where Bob lives. If it snows on either of these two days, the chance that it will snow on each of the next four days increases to $\frac{1}{3}$. If it does not snow on the first two days, the chance of snow on each of the next four days remains $\frac{1}{4}$. What is the probability that it snows at least once during the first six days of January?

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