
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 with center \( C \) is tangent to the positive \( x \)-axis and positive \( y \)-axis and externally tangent to the circle centered at \( (5,0) \) with radius \( 1.5 \). What is the sum of all possible radii of the circle with center \( C \)?

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