
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
Let \(x = 2+\frac{\sqrt{3}}{2+\frac{\sqrt{3}}{2+...}}\). Find \(\frac{1}{(x+1)(x-3)}\). When your answer is in the form \(\frac{A+\sqrt{B}}{C}\), where \(A\), \(B\), and \(C\) are integers, and \(B\) is not divisible by the square of a prime, what is \(|A|+|B|+|C|\)?

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