
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 the side ratio \( A B: A C = 5:4 \), the angle bisector of \( \angle B A C \) intersects side \( B C \) at point \( L \). Find the length of segment \( A L \), given that the length of the vector \( 4 \cdot \overrightarrow{A B} + 5 \cdot \overrightarrow{A C} \) is 2016.

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