
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
In triangle ABC, the incircle touches side AC at point D,
dividing AC into segments AD = 4 units and DC = 5 units. The radius of the circle is given as 3 units. Determine the length of the shortest side of the triangle.
A) 9 units  
B) 10 units  
C) 11 units  
D) 12 units  
E) 13 units

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