
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 \( x = 1 + \frac{\sqrt{3}}{1 + \frac{\sqrt{3}}{1 + \dots}} \). Find the value of \( \frac{1}{(x+2)(x-3)} \). 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}
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