
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 the curve $y= \frac{1}{x}$ and the lines $x=1$, $x=3$, $y=0$ that enclose the closed region $A$, and the lines $x=1$, $x=3$, $y=0$, $y=1$ that enclose the closed region $B$, find the probability that a point $P$ randomly chosen within region $B$ also falls within region $A$.

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