
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
Given two parallel lines at a distance of 15 units from each other, there is a point \( M \) that is 3 units away from one of them. A circle is drawn through the point \( M \) and tangent to both lines. Find the distance between the projections of the center and the point \( M \) onto one of the given lines.

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