
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 final answer is: Given \( m > 2 \), the lines \( l_1: y = \frac{m-2}{m} x + 2 \) and \( l_2: y = -x + 2m \) form a triangle with the y-axis, and the area of this triangle is 30. Find the value of \( m \).

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