
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
Two circles have centers 50 inches apart. The radius of the smaller circle is 8 inches, and the radius of the larger circle is 10 inches. Determine the lengths of the common internal tangent and the common external tangent between the two circles.
A) 46.67 inches and 49.96 inches
B) 45 inches and 50 inches
C) 46 inches and 49 inches
D) 47 inches and 50 inches

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