
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

Given a triangle \( ABC \) with point \( M \) being the midpoint of side \( BC \). Let \(\ell\) be the bisector of the external angle at \( A \) of triangle \( ABC \). The line passing through \( M \) and parallel to \(\ell\) intersects side \( AB \) at point \( K \). Find the length of segment \( AK \), given that \( AB=23 \) and \( AC=8 \).

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