
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
Inside a circle with a radius of 15 cm, a point \( M \) is taken at a distance of 13 cm from the center. A chord is drawn through the point \( M \) with a length of 18 cm. Find the lengths of the segments into which the point \( M \) divides the chord.

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