
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
Mr. Canada chooses a positive real \( a \) uniformly at random from \((0,1]\), chooses a positive real \( b \) uniformly at random from \((0,1]\), and then sets \( c = \frac{a}{a+b} \). What is the probability that \( c \) lies between \(\frac{1}{4}\) and \(\frac{3}{4}\)?

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