
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
Circles with centers $O_{1}$ and $O_{2}$ and equal radii are inscribed at vertices $A$ and $B$ of triangle $ABC$ respectively. The point $O$ is the center of the circle inscribed in triangle $ABC$. These circles touch the side $AB$ at points $K_{1}$, $K_{2}$, and $K$ respectively, where $AK_{1}=4$, $BK_{2}=6$, and $AB=16$.

a) Find the length of segment $AK$.

b) Let the circle centered at $O_{1}$ touch the side $AC$ at point $K_{3}$. Find the angle $CAB$, given that point $O_{1}$ is the center of the circle circumscribed around triangle $OK_{1}K_{3}$.

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