
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
Given circles $A$, $B$, and $C$ are arranged such that each circle is tangent to the other two, with radii $a$, $b$, and $c$, respectively, where $a > b > c$, determine the nature of the expression $\overline{AB} + \overline{BC} - \overline{CA}$.

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