
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
A circle $P$ has a circumference of $18\pi$ meters. Segment $AB$ is a diameter of circle $P$. If the measure of angle $APC$ is $45^{\circ}$, where $C$ is a point on the circle, what is the length, in meters, of segment $AC$?

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