
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 incircle of triangle $A B C$ touches its sides $A B$, $B C$, $C A$ at points $C_{1}$, $A_{1}$, $B_{1}$ respectively. The segment $B B_{1}$ intersects the circle again at point $K$. It is known that $A B = B C = 5$, $A C = 6$. Find $B K$.

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