
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 a triangle \(ABC\) with sides \(|AB| = 3 \text{ cm}\), \(|BC| = 10 \text{ cm}\), and an angle \(\angle ABC = 120^\circ\). Draw all points \(X\) such that the triangle \(BCX\) is isosceles and at the same time, the triangle \(ABX\) is isosceles with the base \(AB\).

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