
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 6 and is centered at $O$. Point $A$ lies outside $\omega$ such that the distance $OA = 15$. The two tangents to $\omega$ from point $A$ are drawn, and points $B$ and $C$ are chosen on them (one on each tangent), such that line $BC$ is tangent to $\omega$. If $BC = 10$, compute $AB + AC$.

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