
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 \( A B C \) with side \( A C = 8 \), a bisector \( B L \) is drawn. It is known that the areas of triangles \( A B L \) and \( B L C \) are in the ratio \( 3: 1 \). Find the bisector \( B L \), for which the height dropped from vertex \( B \) to the base \( A C \) will be the greatest.

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