
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
A line L passes through the point (2, 4) and is intersected by two parallel lines $L_1: 2x - y + 2 = 0$ and $L_2: 2x - y - 3 = 0$. The midpoint of the line segment AB intercepted by $L_1$ and $L_2$ lies exactly on the line $2x - 4y + 13 = 0$. Find the equation of line L.

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