
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
In the first half of 2016, investor Mr. Yuan invested in two stocks, A and B. The probability of making a profit from stock A was $\frac {1}{3}$, and the probability of making a loss was $\frac {2}{3}$. Stock B had a probability of $\frac {1}{4}$ to make a profit and $\frac {3}{4}$ to incur a loss. For stock A, if it made a profit, it would earn 50,000 yuan, and if it made a loss, it would lose 40,000 yuan; for stock B, if it made a profit, it would earn 60,000 yuan, and if it made a loss, it would incur a 50,000 yuan loss.  
(I) Calculate the probability that Mr. Yuan makes a profit from investing in both stocks A and B in the first half of 2016;  
(II) Determine the probability distribution and the mathematical expectation of the total revenue from investing in both stocks A and B for Mr. Yuan in the first half of 2016.

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