
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
In triangle \(ABC\), \(AC = 8\) and \(BC = 5\). A line parallel to the bisector of the external angle at \(C\) passes through the midpoint of side \(AB\) and point \(E\) on side \(AC\). Find \(AE\).

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