
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
The diagram depicts two circles and a square positioned between a pair of parallel lines, 400 units apart. The square has a side length of 279 units, with one side along the lower line. Two circles, tangent to each other and to one of the lines, are also depicted, touching the square at exactly one point each. The upper circle touches a vertex of the square, and has a radius of 65 units. Determine the radius of the lower circle.

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