
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
Find \( \cot^{-1}(1) + \cot^{-1}(3) + \ldots + \cot^{-1}(n^2 + n + 1) + \ldots \), where \( \cot^{-1}(m) \) is taken to be the value in the range \( (0, \frac{\pi}{2}] \).

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