
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
Let \( \mathrm{ABC} \) be a triangle, and let its angle bisectors \( \mathrm{AL} \) and \( \mathrm{BN} \) intersect at point \( \mathrm{O} \). Denote \( h_a \) as the height dropped onto side \( a \), and \( l_a \) as the angle bisector of side \( a \).

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