
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
Two points  $A, B$  are randomly chosen on a circle with radius  $100.$  For a positive integer  $x$ , denote  $P(x)$  as the probability that the length of  $AB$  is less than  $x$ . Find the minimum possible integer value of  $x$  such that  $\text{P}(x) > \frac{2}{3}$ .

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