
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
Let \( C_1 \) and \( C_2 \) be circles defined by
\[
(x-12)^2 + y^2 = 25
\]
and
\[
(x+18)^2 + y^2 = 64,
\]
respectively. What is the length of the shortest line segment \( \overline{RS} \) that is tangent to \( C_1 \) at \( R \) and to \( C_2 \) at \( S \)?

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