
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
The sequence  $(u_n)$  is defined by  $u_1 = 1, u_2 = 2$  and  $u_{n+1} = 3u_n - u_{n-1}$  for  $n \ge 2$ . Set  $v_n =\sum_{k=1}^n \text{arccot }u_k$ . Compute  $\lim_{n\to\infty} v_n$ .

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