
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 a triangle, the angles are in arithmetic progression, and the sides are \( 5, 7, x \). The sum of the possible values of \( x \) equals \( a + \sqrt{b} + \sqrt{c} \), where \( a, b \), and \( c \) are positive integers. What is \( a+b+c \)?
**A)** 36  
**B)** 38  
**C)** 39  
**D)** 42  
**E)** 44

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