
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
The angle bisectors \( A L_{1} \) and \( B L_{2} \) of triangle \( A B C \) intersect at point \( I \). It is known that \( A I : I L_{1} = 3 \) and \( B I : I L_{2} = 2 \). Find the ratio of the sides of triangle \( A B C \).

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