
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
In triangle \(ABC\), the angles \(\angle B = 30^\circ\) and \(\angle A = 90^\circ\) are known. Point \(K\) is marked on side \(AC\), and points \(L\) and \(M\) are marked on side \(BC\) such that \(KL = KM\) (point \(L\) lies on segment \(BM\)).

Find the length of segment \(LM\), given that \(AK = 4\), \(BL = 31\), and \(MC = 3\).

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