
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
Tyler rolls two  $ 4025 $  sided fair dice with sides numbered  $ 1, \dots , 4025 $ . Given that the number on the ﬁrst die is greater than or equal to the number on the second die, what is the probability that the number on the ﬁrst die is less than or equal to  $ 2012 $ ?

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