
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 \( ABC \), the median \( AM \) (the segment connecting vertex \( A \) with the midpoint \( M \) of side \( BC \)) is extended beyond point \( M \) by a length equal to \( AM \). Find the distance from the resulting point to points \( B \) and \( C \) if the sides \( AB \) and \( AC \) are 5 and 4, respectively.

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