
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 \( \mathrm{ABC} \) with \( \mathrm{BK} \) and \( \mathrm{CL} \) as angle bisectors intersecting at point \( M \). It is known that triangle \( \mathrm{AMC} \) is isosceles and one of its angles is 150 degrees. Find the possible value of the perimeter of triangle \( \mathrm{ABC} \), given \( \mathrm{BK} = 4 - 2 \sqrt{3} \).

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