
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
Evaluate  $\textstyle\sum_{n=0}^\infty \mathrm{Arccot}(n^2+n+1)$ , where  $\mathrm{Arccot}\,t$  for  $t \geq 0$  denotes the number  $\theta$  in the interval  $0 < \theta \leq \pi/2$  with  $\cot \theta = t$ .

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