
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 $LM$ if it is known that $AK = 4$, $BL = 31$, and $MC = 3$.

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