
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
For the first five days of January, there is a $\frac{1}{5}$ chance that it will snow where Bob lives. For the next five days, the probability of snow is $\frac{1}{3}$. If the temperature drops below $0^\circ C$ (which happens with probability $\frac{1}{2}$ each day), the probability of snow each day increases by $\frac{1}{10}$. What is the probability that it snows at least once during these ten days?

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