
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
A point $Q$ is randomly selected from the rectangular region with vertices $(0,0), (3,0), (3,1), (0,1)$. What is the probability that $Q$ is closer to the point $(1,0)$ than it is to the point $(4,1)$?

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