
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
An object starts at point $A$, moves $10$ cm in a straight line to $B$, then turns at an angle $\alpha$, which is uniformly distributed over the interval $(0, \pi)$, and moves $8$ cm to $C$. Determine the probability that the distance $AC$ is less than $12$ cm.
A) $\frac{1}{8}$
B) $\frac{1}{6}$
C) $\frac{1}{4}$
D) $\frac{1}{3}$
E) $\frac{1}{2}$

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