
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 the recurrence relation \( x_{k+1} = x_k + \frac{1}{3} \) for \( k = 1, 2, \dots, n-1 \) and \( x_1 = 2 \), find the sum \( x_1 + x_2 + \dots + x_n \).
**A)** \( \frac{n+11}{6} \)  
**B)** \( \frac{n(n+11)}{6} \)  
**C)** \( \frac{n(n+5)}{2} \)  
**D)** \( \frac{n(n+3)}{2} \)  
**E)** \( \frac{n(n+7)}{4} \)

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