
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
Three circles with centers \( A \), \( B \), and \( C \), have radii 2, 3, and 4 respectively. All three circles are tangent to the same line \( m \) at points \( A' \), \( B' \), and \( C' \) respectively, with \( B' \) directly between \( A' \) and \( C' \). Circle centered at \( B \) is externally tangent to the other two circles. Determine the perimeter of quadrilateral \( A' B' C' B \).
A) \( \sqrt{26} + 3\sqrt{2} + 5 \)  
B) \( \sqrt{25} + 5\sqrt{2} + 3 \)  
C) \( \sqrt{26} + 5\sqrt{2} + 3 \)  
D) \( \sqrt{25} + \sqrt{50} + 3 \)

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