
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 sequence $\left\{A_{n}\right\}$ defined by
$$
A_{1}=1, \quad A_{2}=3, \quad A_{n}=4 A_{n-1}-A_{n-2},
$$
find the value of $\sum_{n=1}^{+\infty} \operatorname{arccot} 2 A_{n}^{2}$.

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