
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 jar contains balls, each of which is green, yellow, or purple. The number of purple balls is at least twice the number of yellow balls and at most one fourth the number of green balls. The number of balls that are yellow or purple is at least $75$. Find the minimum number of green balls.
A) 175
B) 200
C) 225
D) 250
E) 275

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