
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
Three straight lines, \( l_{1}, l_{2} \), and \( l_{3} \), have slopes \( \frac{1}{2}, \frac{1}{3} \), and \( \frac{1}{4} \), respectively. All three lines have the same \( y \)-intercept. Find the \( y \)-intercept given that the sum of the \( x \)-intercepts of the three lines is 36.

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