
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
Circle $\omega'$ has a radius of 4 and is centered at $O$. Point $A$ is located such that $OA = 15$. Two tangents from $A$ to $\omega'$ are drawn, with points $B$ and $C$ at each tangent such that line $BC$ is tangent to $\omega'$, with $\omega'$ positioned outside triangle $ABC$. Find $AB + AC$ if $BC = 8$.

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