
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
If an urn is divided into two compartments and one compartment contains \(v_{1}\) red and \(f_{1}\) white balls, while the other compartment contains \(v_{2}\) red and \(f_{2}\) white balls, what is the probability of randomly drawing a red ball? What would be the probability if there were no partition in the urn, and under what conditions would the two probabilities be equal?

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