
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
Point \((x,y)\) is randomly picked from the rectangular region with vertices at \((0,0),(2010,0),(2010,2009),\) and \((0,2009)\). What is the probability that \(x > 2y\) and \(y > 500\)? Express your answer as a common fraction.

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