
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
Two people, A and B, simultaneously work on the same mathematics competition problem. If they solve it correctly, the teacher awards a prize of 190 yuan. The reward goes to the one who solves it correctly, and if both solve it correctly, the prize is split equally. Given that the probability of A solving it correctly is $\frac{3}{4}$ and the probability of B solving it correctly is $\frac{4}{5}$, what is the most reasonable prize distribution amount?

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