
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 of radius \( r \) touches a certain line at a point \( M \). On this line, points \( A \) and \( B \) are taken on opposite sides of \( M \), such that \( M A = MB = a \).

Find the radius of the circle passing through points \( A \) and \( B \) and touching the given circle.

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