
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 vertices of a right-angled triangle are on a circle of radius  $R$  and the sides of the triangle are tangent to another circle of radius  $r$  (this is the circle that is inside triangle). If the lengths of the sides about the right angles are 16 and 30, determine the value of  $R+r$ .

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