
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
Two chords of a circle, each equal to 12 and 16, are drawn through the ends of the diameter and intersect on the circumference. Find the distances from the center of the circle to these chords.

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