
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
Given a bag containing white and red balls with a total of $n$ balls and $m$ white balls among them. If two balls are drawn randomly, the probability that at least one ball is red is $\frac{3}{5}$. If the drawing is with replacement, and each draw consists of one ball for a total of 6 draws, then the expected number of times a white ball is drawn is 4. Now, drawing from the bag without replacement, two balls are drawn one by one. What is the probability of drawing another red ball given that the first ball drawn is red?

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