
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
It is known that bag A contains $m$ red balls and $n$ white balls, and bag B contains $3$ red balls and $4$ white balls. First, one ball is randomly taken from bag A and placed into bag B, then one ball is randomly taken from bag B. If the probability of drawing a red ball is $\frac{15}{32}$, calculate the probability of drawing a red ball from bag A.

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