
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
A triangle \( ABC \) is given. It is known that \( AB=4 \), \( AC=2 \), and \( BC=3 \). The angle bisector of \( \angle BAC \) intersects side \( BC \) at point \( K \). A line passing through point \( B \) parallel to \( AC \) intersects the extension of the bisector \( AK \) at point \( M \). Find \( KM \).

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