
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
Let  $S$  be the set of all 3-tuples  $(a,b,c)$  that satisfy  $a+b+c=3000$  and  $a,b,c>0$ .  If one of these 3-tuples is chosen at random, what's the probability that  $a,b$  or  $c$  is greater than or equal to 2,500?

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