
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 line $l_1$: $y=2x$ and the line $l_2$: $ax+by+c=0$ ($abc\neq0$) are perpendicular to each other. When $a$, $b$, and $c$ form an arithmetic sequence, the area $S$ of the triangle formed by lines $l_1$, $l_2$, and the y-axis is \_\_\_\_\_\_.

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