
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
The radius of the circle circumscribed around the triangle $K L M$ is $R$. A line is drawn through vertex $L$, perpendicular to the side $K M$. This line intersects at points $A$ and $B$ the perpendicular bisectors of the sides $K L$ and $L M$. It is known that $A L = a$. Find $B L$.

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