
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 point \( P \) is located 7 cm away from the center of a circle with a radius of 11 cm. A chord of length 18 cm passes through this point. What are the lengths of the segments into which the chord is divided by the point \( P \)?

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